Introduced feral cat (Felis catus) populations are an important threat to many island vertebrate populations and to bird species in particular. Elimination of feral cat populations is desirable in most of these ecosystems. Release of a parasite species in these mostly immune-naive populations is thought to be an efficient eradication measure. Such an approach is theoretically investigated here, using a mathematical model that describes the effects of introducing a virus into the cat population on population dynamics of both the cat and its prey. We studied the effects of two types of introduced feline viruses: Feline Immunodeficiency Virus and Feline Leukemia Virus, both of which are good candidates for eradicating a cat population. Results show that eradication is possible with Feline Leukemia Virus, if natural immunity is sufficiently low. Feline Immunodeficiency Virus cannot fully eradicate cat populations, but can be an effective agent for long-term control of cat populations on islands where total cat eradication is not possible (e.g., there is a high likelihood of continued introduction of cats) or not desirable (e.g., when rats are present). Culling, which by itself would require a very prolonged and logistically demanding effort to eliminate cat populations, may be more efficient when applied simultaneously with virus introduction.