One consequence of the increasing number of small satellite missions is an increasing demand for high data rate downlinks. As the satellites transmit at high data rates, ground-side receivers need to demodulate the transmitted data as quickly as possible. While application specific hardware can be designed, software defined radio solutions for ground stations are attractive for their flexibility, adaptability, and portability. Another industry trend is the increasing use of Graphics Processing Units (GPUs) in general-purpose processing. By performing many operations simultaneously, GPUs are capable of accelerating processing when given a problem that can be implemented in a parallel manner. Furthermore, once a parallel algorithm is implemented, further speedups are possible by increasing hardware resources without need for any revision in the algorithm. This project combines the above ideas by implementing a software defined radio algorithm to quickly demodulate high-speed data on a GPU. It demonstrates the viability of the GPU in software defined radio applications and particularly in the area of fast demodulation.