In this musical comedy, a girl with a lively imagination gets in hot water when she tries to make her tall tales real.
Gloria Harkinson (Deanna Durbin) is the teenage daughter of Gwen Taylor (Gail Patrick), a well-known Hollywood actress who has shipped Gloria off to a boarding school in Switzerland to keep the girl out of the public eye, partly for her well being, and party because Gwen would prefer people not to know that she's old enough to have a teenage daughter.
Gloria amuses herself and earns the awestruck admiration of her schoolmates when she begins spinning increasingly remarkable tales about the globe-trotting adventures of her millionaire father. However, in reality Gloria has no father, and after some time, her friends become skeptical and demand some sort of physical evidence that he exists.
Gloria makes the acquaintance of Richard Todd (Herbert Marshall), a British composer, and she asks him if he wouldn't mind posing as her dad so that her friends could meet the man they've heard so much about. Richard agrees, but the scheme doesn't go quite as Gloria had hoped.
Mad About Music was later remade as The Toy Tiger (1956), with Gloria turned into a young boy named Timmie, and the songs removed.