A ship carrying a Swiss family from Bern—consisting of Father, Mother, and their three sons—embarks on a journey to a colony in New Guinea to escape the turmoil of the Napoleonic Wars. Unfortunately, their voyage takes a perilous turn when pirates attack, leading to the crew abandoning the ship. The vessel ultimately runs aground on the rocks of an uninhabited island. The family, joined by the captain's two Great Danes, manages to reach the shore. Father, along with his eldest son, Fritz, and middle son, Ernst, work together to salvage supplies and livestock from the wreckage. When the pirates discover their ship, Father cleverly deters them by hoisting a quarantine flag, hinting at the presence of Bubonic plague on board.
As the family settles into their new surroundings, they quickly learn that this island harbors a wide variety of wildlife, most notably a lurking, dangerous tiger. In a bid to ensure their safety and comfort, Father, Fritz, and Ernst build an intricate tree house that is equipped with a water wheel. The youngest son, Francis, takes to collecting a menagerie of animals, including a young Asian elephant, a monkey, and an ostrich. Ernst speculates that the island may have once linked Africa and Asia via a land bridge. While the family begins to thrive in their natural setting, Father reflects that they have found everything they need in life, but Mother expresses concern for her sons' future and whether they will marry and have families if they remain stranded. She agrees to let Fritz and Ernst explore the island in a makeshift outrigger boat to search for possible rescues.
During their adventurous expedition, the brothers unexpectedly encounter pirates who have captured another ship, taking the captain and a cabin boy hostage. They manage to free the cabin boy, only to discover that she is actually a girl named Roberta. To evade the pirates, her grandfather disguised her as a boy. They face numerous challenges, including a terrifying encounter with a green anaconda, but remain determined to navigate their way through the jungle. Following Fritz's lead, they rescue a zebra from dire situations and manage to return to their tree house just in time for Christmas.
Aware that the pirates will likely pursue Roberta, the family strategically scuttles their wrecked ship to conceal their location. They fortify a rocky clifftop, complete with defenses and booby traps. Tensions rise as Fritz and Ernst vie for Roberta's affection. While she longs to return to London once ransomed, Ernst hopes to attend school there, and Fritz dreams of building a home in New Guinea. Despite their rivalry, a burgeoning romance develops between Fritz and Roberta, leading to confrontations. To ease the mounting tension, Father initiates a celebratory holiday. On this particular night, Francis successfully captures the elusive tiger in one of the traps they dug.
The holiday festivities kick off with an exhilarating race, showcasing the boys and Roberta riding various animals. However, the celebratory atmosphere is disrupted when the pirates, alerted by the sound of the starting pistol, invade their refuge. The family retreats to their defenses, using their myriad traps against the incoming pirates. Pirate captain Kuala demands that they surrender Roberta, while his men orchestrate a surprise attack from behind. Just as it seems the family is overwhelmed, a ship helmed by Roberta's grandfather arrives, unleashing cannon fire that obliterates the pirates and their ship.
The captain offers Ernst a chance to attend a university in London and presents the family with options to either return to Europe or proceed to New Guinea. However, Father and Mother express their desire to remain on the island a while longer, wanting to keep Francis with them for a few additional years. The captain speculates that the island might become a new colony, with Father as a possible governor. In a heartwarming twist, Fritz and Roberta choose to stay, while the family bids farewell to Ernst as he departs for England with the captain and the crew.
