Due to their weak received signal power, Global Positioning System (GPS) signals are vulnerable to radio frequency interference. Adaptive beam and null steering of the gain pattern of a GPS antenna array can significantly increase the resistance of GPS sensors to signal interference and jamming. Since adaptive array processing requires intensive computational power, beamsteering GPS receivers were usually implemented using hardware such as field-programmable gate arrays (FPGAs). However, a software implementation using general-purpose processors is much more desirable because of its flexibility and cost effectiveness. This paper presents a GPS software-defined radio (SDR) with adaptive beamsteering capability for anti-jam applications. The GPS SDR design is based on an optimized desktop parallel processing architecture using a quad-core Central Processing Unit (CPU) coupled with a new generation Graphics Processing Unit (GPU) having massively parallel processors. This GPS SDR demonstrates sufficient computational capability to support a four-element antenna array and future GPS L5 signal processing in real time. After providing the details of our design and optimization schemes for future GPU-based GPS SDR developments, the jamming resistance of our GPS SDR under synthetic wideband jamming is presented. Since the GPS SDR uses commercial-off-the-shelf hardware and processors, it can be easily adopted in civil GPS applications requiring anti-jam capabilities.