The domestic cat is an invasive species that often causes great impacts where introduced due to its high predatory and reproductive potential, especially on islands. In this study, carried out on Ilha Grande (RJ, Brazil), we aimed to: i) estimate the population density of domestic cats, ii) calculate the number of animals preyed upon annually by domestic cats, and iii) evaluate the efficiency of methods to control the cat population. We used the Vortex program to project the population growth of domestic cats in fifty years, and simulated different scenarios of population control (without control, castration, spay and harvest). Population density of owned cats was 662 cats/km(2). The annual predation rate was 1.97 prey animals/cat which is an average of 1497.96 prey/year. The population would only be reduced if 70% of females were spayed or removed annually. Measures to control the domestic cat population must be undertaken urgently, since uncontrolled growth of this predator has the potential to seriously impact the biodiversity of Ilha Grande.