Combined with Frequency-Modulated Continuous-Wave (FMCW) technology, airborne forward-looking Synthetic Aperture Radar (SAR) with linear array antennas can obtain the image in front of the aircraft and also have the advantages of FMCW radar such as small size and lightweight. Moreover, it is suitable to be installed on platform like helicopter and small unmanned aerial vehicle. Motion compensation for forward-looking SAR with linear array antennas is one of the key problems to obtain the image in front of the aircraft in practice. This paper analyses the influence of motion error in aircraft on echo model based on the geometry of forward looking SAR with linear array antennas, and proposes a motion compensation scheme. Moreover, the compensation scheme is applicable to an improved frequency scaling algorithm (FSA) for FMCW forward looking SAR with linear array antennas. Finally, the compensation scheme is verified with the simulation.