Popeye, played by Robin Williams, is a strong sailor who arrives at the quaint coastal village of Sweethaven in search of his long-lost father. However, his arrival is met with fear and suspicion from the local townsfolk, who see him as an outsider, leading to a series of comedic yet tumultuous encounters. Almost immediately, Popeye finds himself at odds with a greedy taxman (Donald Moffat), who promptly targets him for tribute. Seeking refuge, Popeye rents a room at the boarding house owned by the Oyl family. Here, he meets Olive, played by Shelley Duvall, who, unbeknownst to him, is preparing for her engagement party with the town's powerful bully, Captain Bluto (Paul L. Smith), who exerts control on behalf of the mysterious Commodore.
As Popeye attempts to adjust to the local customs and partake in breakfast at a diner, he showcases his impressive strength by defending himself against a group of unruly ruffians, earning a mix of respect and fear from the customers around him. On the night of Olive's engagement bash, tension rises as she feels trapped by her brutish fiancé, Bluto, and sneaks out to meet Popeye. Their budding friendship takes an unexpected turn when they find an abandoned baby in a basket on the doorstep. The note attached reveals that the baby’s mother is unable to care for him and wishes for Popeye to step in as his father. Embracing this opportunity, Popeye names the child Swee'Pea and returns to the Oyl home with Olive, but not without provoking Bluto's wrath, leading to a chaotic showdown that culminates in Bluto's destructive rage against the Oyl family’s property.
As a reaction to the overwhelming pressure, the Oyls lose their home to the taxman, pushing Castor, the Oyl family’s son, to take a dangerous risk by challenging the local heavyweight boxer, Oxblood Oxheart (Peter Bray), in a bid to earn money for the family. Unfortunately, Castor is no match for the seasoned fighter and is brutally defeated. Rising to the occasion, Popeye steps into the ring and triumphantly defeats Oxheart, slowly winning the grudging respect of the townsfolk. Under the glow of newfound camaraderie, Popeye and Olive share a tender moment as they lull Swee'Pea to sleep with a song, marking a brief respite in tumultuous events.
The following day takes a bizarre turn when Olive discovers that Swee'Pea possesses the unusual ability to predict the future by whistling. This revelation catches the ear of the local schemer Wimpy (Paul Dooley), who takes Swee'Pea for a walk, only to exploit his gift for gambling at the horse races. Outraged and feeling protective, Popeye confronts the ramifications of Swee’Pea's newfound fame. His frustrations boil over as he pushes the taxman into the water, earning an unexpected celebration from the townsfolk amid the chaos. But trouble escalates when Wimpy, under duress from Bluto, kidnaps Swee'Pea and takes him aboard the Commodore's ship.
In a turn of fate, Popeye discovers that the Commodore is actually his father, Poopdeck Pappy (Ray Walston). Initially dismissive of Popeye’s claims, he attempts to induct his son into enjoying the family’s supposed source of strength—canned spinach—only to face rejection from the spinach-hating Popeye. As Bluto escalates his villainy by capturing Olive and setting sail for treasure, Popeye, joined by Pappy, Wimpy, and the Oyl family, gives chase to thwart Bluto’s evil intentions.
The confrontation reaches its climactic peak on the desolate Scab Island, where Popeye and Bluto engage in a fierce battle. With the stakes rising high, Pappy uncovers his long-lost treasure, laden with sentimental items from Popeye’s childhood. However, their duel attracts the attention of a giant octopus, ramping up the danger. In a critical moment, as Bluto’s strength seems insurmountable, Pappy’s decisive action to throw a can of spinach to Popeye triggers his change of fate. The very food he despises becomes the key to his strength. Empowered by the spinach, Popeye delivers a singular blow to Bluto and deals with the monstrous octopus in an epic showdown, culminating in a well-deserved celebration of strength, heroism, and the marvelous journey of embracing one's heritage, ultimately chanting, > "I yam what I yam, and that's all that I yam!"
