Fourteen-year-old Dave Mitchell lives in a Manhattan apartment with his parents. His father, Pop, a small, energetic lawyer, lectures Dave about the virtues of dog ownership and outdoor activity. His mother, Mom, is thin and quiet, prone to asthma attacks that Dave believes are triggered by Pop's shouting rather than dust.
After Pop blows up over a Belafonte record Dave bought with babysitting money, Dave storms out and visits Kate, an eccentric older woman who houses stray cats. The neighborhood children call her "Crazy Kate the Cat Woman." Dave first met Kate years earlier when she pulled him back from an oncoming car, and since then they have looked out for each other.
That day, Dave finds a sleek tiger-striped tomcat hiding under Kate's sofa, picks him up on impulse, and decides to take him home. Pop sputters, but Dave promises to keep the cat in his room and sweep up hair to protect Mom. He names the animal simply "Cat," reasoning that no name will make a cat come when called.
Cat adjusts easily but soon begins exploring outdoors. When Cat fails to return one morning, Dave tracks him to a basement on 21st Street and finds him locked in a wire cage. A young man around 19 picks the padlock with a paper clip, frees Cat, and urges Dave to leave. Dave's attempts to report the stranger backfire: The building superintendent grows suspicious of Dave, and the local paper describes a cellar robbery suspect matching his appearance. Days later, the paper reveals the thief is Tom Ransom, who stole a suitcase on a dare and was caught returning it. Feeling responsible, Dave writes Tom thanking him for freeing Cat and offering Pop's services as a lawyer.
Tom writes back from a Young Men's Christian Association residence on 23rd Street where the Youth Board has placed him. Dave's closest friend is Nick, who lives above his father's grocery around the corner. On the first hot Saturday in May, Dave and Nick take Cat to Coney Island, where three girls picnic nearby. Nick flirts with a blonde, and a quiet girl named Mary strokes Cat and asks about him. Nick later arranges a double date, but it turns sour when he mocks Dave throughout. On the walk home Dave punches Nick, and they brawl until bystanders separate them. They stop speaking.
Tom appears at Dave's stoop one Saturday, restless before his summer job at a Brooklyn filling station begins. Dave introduces Tom to Mom, and they explore Inwood Park at Manhattan's northern tip, eating sandwiches above the Hudson. Tom quietly remarks that having a mother at home must be pleasant, hinting at his own absent family.
Over the summer, Dave and Nick gradually resume speaking, though they are no longer close. Tom invites Dave to meet his girlfriend Hilda at Coney Island. While Tom swims far out, Hilda reveals his history: Tom attended New York University for about a year and a half before his father, who lives in the Midwest with a stepmother, told him not to come home at Christmas. After a dorm water fight the other parents paid for but Tom's father ignored, Tom quit school and vanished. Dave offers to ask Pop for advice, and Pop tells Dave to have Tom call his office.
Cat comes home limping after a street fight. Kate tells Dave that Cat must be neutered or he will be killed within a year or two. Dave rejects the idea, but Cat keeps fighting and is found one morning with a deep gash from shoulder to leg. Mom tells Dave that Cat belongs to him and he must do what is best. At the veterinary hospital, Dave agrees to have Cat neutered during surgery to repair the leg. He carries Cat home and cries into his pillow. Cat hops off the bed on three good legs and carries on.
In August, Dave runs into Mary at a record store. Both have forgotten each other's names. Dave suggests they see
West Side Story, and they are thrilled by the performance. Unable to ask for Mary's phone number on the noisy subway, Dave proposes meeting at the beach on Columbus Day.
Tom reports that he visited Pop's office. Seeing how Dave complains about his own father has made Tom reconsider his own. Pop advised Tom to write his father a long, honest letter about quitting school and his legal trouble. Weeks later, Tom's letter comes back stamped with no forwarding address: His father and stepmother have simply left. Pop helps Tom move forward, securing him a job at a neighborhood flower shop.
Before the family's vacation to Connecticut, Cat escapes through an open car window on the highway. Pop laughs and refuses to stop, but Dave jumps from the barely moving car and grabs Cat from the roadside. He walks miles back toward the city, arriving at Kate's apartment after dark to find his parents already there. Pop admits he should not have laughed, picks up Cat, and declares him one of the family.
Dave starts at Charles Evans Hughes High School and befriends Ben Alstein, a boy in the school's science track. They explore the city together, from the Fulton Fish Market to the Bronx Zoo. When Cat kills one of Ben's pet salamanders, the boys clash but reconcile over their research.
On a bitterly cold Columbus Day, Dave meets Mary on the deserted Coney Island boardwalk. They retreat to her nearby house, where Dave meets Nina, Mary's mother, a bohemian woman who grew up on the Left Bank of Paris and dismisses American schools as childish. Mary confides she loves science, which Nina cannot appreciate. Dave and Mary bike to the Staten Island ferry and spend the day exploring.
On Thanksgiving, the Mitchells host Tom and Kate for dinner. That evening, a telegram reveals Kate's estranged brother has died and left her his fortune. Reporters descend on Kate's apartment, and a photographer accidentally steps on her orange kitten, mortally injuring it. Kate mercifully kills the suffering animal and screams at the reporters to leave. Pop clears out the press, takes two stray kittens home, and arranges for Kate's inheritance to go into a bank trust. Kate mentions leaving money to the Children's Aid Society, noting that stray children need looking after as well as cats.
Dave's plan to meet Mary on Election Day collapses because he has the flu and no way to reach her. During Christmas vacation, Mary calls from a phone booth in Macy's, stranded without money. Dave meets her at the store and brings her home for dinner. She reveals she found his number by searching through all the Mitchells in the Manhattan phone book weeks earlier.
The two stray kittens settle into the Mitchell home. Dave and Pop still clash but are learning restraint, especially since Mom's asthma worsens during their fights. Tom tells Dave they argue because they are alike, both impatient and curious. Late one evening, Tom and Hilda arrive to announce their engagement. Tom plans to enlist in the Army for three years, choosing a specialist school in Air Defense Command that would keep him near New York and let him continue night school. Pop produces champagne and toasts the couple. Dave raises his soda and proposes a toast to Cat, because Tom would not be standing there if it were not for Cat. Everyone drinks. Cat sits down and licks his paw.