Mosquitoes are vectors for many diseases that cause significant mortality and morbidity across the globe such as malaria, dengue fever and Zika. As mosquito populations expand their range into new areas, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population densities. With new technology, creating target specific gene modification may now be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established low-density mosquito populations. Our model consists of two life stages (aquatic and adult), which are further divided into three genetically distinct groups: heterogeneous and homogeneous transgenic alleles that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations.