In this paper the authors present a solution based on a small and lightweight computing platform equipped with a graphics processing unit (GPU) which allows the possibility of performing a real-time fully focused SAR algorithm. The presented system is dedicated for airborne SAR applications including small SAR systems dedicated for medium-sized unmanned aerial vehicle (UAV) platforms. The proposed solution also reduces the need for a storage system. In the paper real SAR results obtained using a Frequency Modulation Continuous Wave (FMCW) radar demonstrator operating at 35 GHz carrier frequency with 1GHz bandwidth are presented. As a radar carrier an airborne platform was used. The presented SAR radar demonstrator was developed by the Warsaw University of Technology in cooperation with the Air Force Institute of Technology, Warsaw, Poland.