Immediately after a baby girl is discovered on the steps of a New York City orphanage, a matron notifies Professor Peter Vincent at the Institute of Child Psychology of her arrival. Vincent and his colleague, Dr. Woodring, examine the infant and, satisfied that she is "perfect," take her to the Institute, where she becomes the subject of a long-term experiment. Over the next six years, Vincent, Woodring and fellow Institute researchers Dr. and Mrs. Catty, Rhoda Kittereck, and Professors Endicott and Richards expose the orphan, whom they have named Alpha, to a rigorous schedule of lessons and controlled play. Under the loving if rigid tutelage of the researchers, Alpha quickly learns Chinese, music, chess, math and history. When Alpha, who has never been outside the Institute's walls, turns six, Vincent invites the New York Morning Transcript to write about her, and Transcript editor Ed Vincent assigns ne'er-do-well reporter Mike Regan, a Harvard graduate, to the story. Mike interviews Alpha and, while impressed with her vast knowledge, questions whether she is happy living in a world without "magic." Alpha is both intrigued and disturbed by Mike's comments and, later that night, slips out of the Institute. With help from a policeman and some Chinese merchants, Alpha, who refers to Mike as her father, tracks the reporter to a boxing match. There Alpha asks Mike to prove his statements regarding the realness of magic, and the bemused Mike walks the girl over to Times Square. Though not thoroughly convinced that she is witnessing magic, Alpha is impressed by the sights and sounds of the busy streets. Mike, who calls Alpha "Professor," then takes her to the nightclub where his girl friend, Katie Mallory, works as a singer. Instantly jealous, Alpha snubs Katie, then indulges in her first plate of spaghetti. When Alpha asks Mike if he likes Katie more than he likes her, Mike refuses to answer, prompting Alpha to burst into tears. While Katie comforts the girl, explaining that the big-hearted if irresponsible Mike is capable of loving them both, Mike telephones the Institute. The researchers, who have been trying desperately to find Alpha, are relieved to hear she is safe, but break the news that because Mrs. Catty has contracted measles and the Institute has been placed under quarantine, Mike has to continue his babysitting chores. Mike begs Katie to care for Alpha, but, determined to teach Mike a lesson in responsibility, she refuses. Soon after Mike settles Alpha into his apartment, Ed telephones with orders to cover the prison escape of Packy Roos, a petty criminal who Mike suspects was framed for murder. Then, just as Vincent calls with a long list of instructions for Mike, Alpha vomits up her spaghetti. After the harried Mike takes off to find Packy, leaving Alpha alone, a gun-wielding Packy sneaks into his apartment. To keep Alpha quiet, the semi-literate Packy offers to read a book of fairy tales to her. Alpha soon takes over the reading chores, however, and by the time Mike returns, the two have become fast friends. Brandishing his gun, Packy tells Mike that a gangster named Lefty Moran framed him and insists that Mike go find him. The next morning, Mike returns to the apartment, empty-handed and hungry, and is forced by Katie to prepare breakfast for everyone. After six more hours of searching, Mike finally drags Lefty back to the apartment. Feeling vengeful, Packy is about to shoot Lefty when the ever-logical Alpha convinces him that he is too smart to commit such a dumb act. Instead, Packy forces Lefty to write a confession, then calls the police. At the same time, the Institute quarantine is lifted, and Vincent and the other researchers rush to collect Alpha. The researchers soon realize how much Mike means to Alpha when she breaks down in tears at the thought of leaving him. Alpha tells Mike that she loves him, but Mike, afraid of his feelings, assures her that she can live without him. Later, a guilt-ridden Mike asks Ed for a transfer to Washington, D.C., unaware that Alpha has become seriously ill with grief. Just as Mike is about to depart, Packy shows up with gifts for Alpha. Packy is disgusted by Mike's rejection of Alpha and goes to the Institute to see her. When he learns about her condition, he determines to reunite her with Mike and leaves to intercept Mike's train. Mike, meanwhile, encounters a young boy and his mother on the train and suddenly realizes he cannot live without Alpha. After rushing back to the Institute, Mike throws himself into Alpha's eager arms, and all are moved by their tearful, happy reunion.