A ship carrying a Swiss family from Bern—consisting of the Father, the Mother, and their three sons—sets sail on a journey to relocate to a colony in New Guinea. This move is primarily motivated by their desire to escape the chaos of the Napoleonic Wars. However, their voyage takes a perilous turn when they are unexpectedly attacked by pirates. Following this harrowing event, the crew abandons ship, leaving the family to fend for themselves. Ultimately, the vessel runs aground on rocks, leaving them stranded on a desolate and uninhabited island. Together with the captain's two loyal Great Danes, the family makes the arduous trek to shore.
Once ashore, the Father, along with the eldest son, Fritz (Tommy Kirk), and the middle son, Ernst (James MacArthur), does what they can to salvage supplies and livestock from the wreckage. Meanwhile, the pirates soon discover the shipwreck, but the Father cleverly wards them off by hoisting a quarantine flag, suggesting that Bubonic plague has invaded their vessel.
As the family begins to adapt to their new surroundings, they encounter a plethora of wildlife, including a formidable tiger that lurks among the trees. To establish safety and comfort, the Father, Fritz, and Ernst work together to construct an elaborate tree house equipped with a functioning water wheel. Youngest son Francis (Kevin Corcoran) busily collects an assortment of animals, ranging from a young Asian elephant to a mischievous monkey and an ostrich. Ernst theorizes about the island's geological past, speculating that it may have once been part of a land bridge connecting Africa and Asia. As the family begins to settle into their new life, the Father expresses his belief that by returning to a more simplistic way of life, they have discovered true happiness. However, the Mother harbors worries that her sons might never find wives or start families if their isolation continues. This leads her to permit Fritz and Ernst to embark on an adventure to circumnavigate the island in a makeshift outrigger boat in search of other settlements.
During their thrilling expedition, the brothers inadvertently stumble upon the very pirates that threatened their lives. These pirates have captured another ship, taking its captain and cabin boy hostage. In a daring move, Fritz and Ernst manage to rescue the cabin boy, only to discover that they are actually rescuing a girl named Roberta. The crew had disguised her as a boy to protect her from the pirates. Just as they're about to escape, they learn that the pirates are onto them and must flee deep into the jungle. The siblings even face off against a massive green anaconda, persevering through the challenges they encounter along the way. As they navigate their way back, they overcome personal differences and arrive home with a zebra they rescued from a perilous situation.
To prepare for a potential pirate assault, the family decides to scuttle their wrecked ship to conceal their whereabouts. They then fortify a rocky outcrop, setting traps and defenses to protect themselves. Tensions rise as Fritz and Ernst find themselves vying for Roberta's affection. Although Roberta believes her grandfather will come back for her once the ransom is paid, she feels a pull towards Ernst, who dreams of studying in London. Yet, there is an undeniable chemistry blossoming between Fritz and Roberta, leading to rivalry and conflict between the brothers over her.
To relieve some of the mounting tension, Father proposes a holiday celebration. The evening culminates in a festive race where the boys, alongside Roberta, ride various animals, adding a spirit of adventure to the celebrations. Unbeknownst to the family, the pirates, sailing nearby, catch wind of the cacophonous festivities. As they invade, Kuala, the pirate captain, demands the hand of Roberta. The family's fortifications are put to the test as they fall victim to the traps they set, creating chaos on the cliffs above.
However, just as the situation seems dire, a ship commanded by Roberta's grandfather arrives, delivering a barrage of cannon fire that scatters the pirates and saves the islanders. Following this tumultuous encounter, the captain offers to help Ernst gain admission to a university in London, inviting the rest of the family to make a choice between returning to Europe or continuing their journey to New Guinea. Ultimately, Father and Mother express their desire to remain on the island a while longer, choosing to keep Francis with them for a few more years. As they bid a heartfelt goodbye to Ernst, who embarks on a new adventure with the captain and crew, Fritz and Roberta also decide to stay, sealing their bond with the island that has now become their home.
