Wilbur "Wilby" Daniels is a boy who is misunderstood by his father, Wilson. Wilson thinks Wilby is crazy half the time because of his elder son's often dangerous inventions. As a retired mailman who often ran afoul of canines, he has a hatred of dogs, and he simply cannot understand why his younger son, Montgomery ("Moochie"), would want a dog.
Wilby and his rival Buzz Miller go with a French girl named Francesca Andrassé to the local museum. Wilby gets separated from the other two, who leave without him. Wilby encounters former acquaintance Professor Plumcutt (whose newspaper Wilby used to deliver), who tells him all about mystical ancient beliefs, including the legend of the Borgia family, who used shape-shifting as a weapon against their enemies.
On the way out, Wilby collides with a table that holds a display case of jewelry. He accidentally ends up with one of the rings in the cuff of his pants. It is the cursed Borgia ring, and no sooner does he read the inscription on it ("In canis corpore transmuto", which, unknown to Wilby, means, "Into a dog's body I change") then he transforms into the Shaggy Dog, named Chiffon, who is Francesca's shaggy "Bratislavian sheepdog", a.k.a Old English Sheepdog. Confused, Wilby, as a dog, goes to Professor Plumcutt, who says Wilby has invoked the Borgia curse upon himself, which can only be broken through a heroic act of selflessness. After getting chased out of his own house by his enraged father, who fails to recognize him as a dog, Wilby has a series of misadventures while switching back and forth between human form and dog form. Only Moochie and Professor Plumcutt know his true identity, as Wilby has spoken to them both in dog form. While at a local dance in his human form, he accidentally transforms himself into a dog.
Francesca sees that Chiffon has been acting strangely, and she asks her adoptive father, Dr. Valasky, to watch over Chiffon for the night. As she exits, a secretive associate of Dr. Valasky named Thurm enters. Wilby, as a dog, overhears Thurm and Dr. Valasky discuss plans to steal a government secret.
The next day, Wilby, as a dog, tells Moochie about the spies. Wilby reveals the secret to his dumbfounded father. As Wilby and Moochie discuss what to do next, Francesca's butler Stefano comes out and drags Wilby into the house. Moochie runs to his father to get help, who goes to the authorities, until Wilson suddenly finds himself accused of being either crazy or a spy.
Stefano and Francesca's adoptive father, Dr. Valasky, are discussing plans to steal a government secret, and Wilby, as a dog, overhears. Unfortunately for him, he transforms into human Wilby right in front of the spies and has been discovered, but not before he hears Dr. Valasky expressing his wish to get rid of his own daughter.
The spies angrily capture Wilby and force Francesca to leave with them, leaving the human Wilby bound and gagged in the closet at once. Fortunately, Moochie sneaks into the house just after Dr. Valasky, Stefano and Francesca leave, and discovers Wilby, who is transformed into a dog, still bound and gagged in the closet.
When Buzz appears at the Valasky residence to take Francesca on a date, Wilby, still in his dog form, steals Buzz's hot rod automobile. Buzz reports this to Officers Hansen and Kelly, who are in disbelief until they see the shaggy dog driving Buzz's hot rod. Wilson and Moochie follow Buzz and the police, who end up chasing everyone. The spies attempt to leave aboard a boat, but the police call in the harbor patrol to apprehend Dr. Valasky and stop his boat. Wilby, in his dog form, swims up and wrestles with the men, as Francesca gets knocked out of the boat. He then saves her life and drags her ashore, which finally breaks the curse of dog form. When Francesca regains her consciousness, Buzz tries to take credit for saving her. This angers Wilby, who is still a dog, so much that he attacks Buzz. Seconds later, Buzz is surprised to find himself wrestling with the real human Wilby, and the real Chiffon reappears. Since Chiffon is soaking wet, Francesca concludes that he has really saved her from the ocean and she hugs and praises him.
Now that Wilson and Chiffon are declared heroes, Francesca is able to leave for Paris without her evil adoptive father and former butler, both of whom have been arrested for espionage; and she gives Chiffon to the Daniels family for them to keep as her way of thanking them. Since Wilson has gotten such commendation for foiling a spy ring because of "his love of dogs," he has a change of heart over his hatred of dogs, a promise to change his ways, and a sense of humor, while he also realizes that his dog-hating attitude isn't really good anymore, so he allows Moochie to care for Chiffon, as he wanted a dog all along. Wilby and Buzz decide to forget their rivalry over Francesca and resume their friendship instead.