The threat of invasive plant species in island populations prompts the need to better understand their population genetics and dynamics. In the Galapagos islands, this is exemplified by the introduced guava (Psidium guajava), considered one of the greatest threats to the local biodiversity due to its effective spread in the archipelago and its ability to outcompete endemic species. To better understand its history and genetics, we analyzed individuals from three inhabited islands in the Galapagos archipelago with 11 SSR markers. Our results reveal similar genetic diversity between islands, and the populations appear to be distinct: the islands of San Cristobal and Isabela are genetically different while the population of Santa Cruz is a mixture from both. Additional evidence for genetic bottlenecks and the inference of introduction events suggests an original introduction of the species in San Cristobal, from where it was later introduced to Isabela, and finally into Santa Cruz. Alternatively, a second introduction in Isabela might have occurred. These results are contrasted with the historical record, providing a first overview of the history of P. guajava in the Galapagos islands and its current population dynamics.