A Ku-band FMCW SAR system is demonstrated which has the capability of real- time processing with the application of single high-performance multi-core DSP. The navigational data of platform movement, which particularly used for high precision motion compensation, is accurately measured by GPS and accelerometer. Furthermore, to realize the real-time processing, the parallel processing approach based on multicore DSP is presented in detail, also the time consumptions of key steps are minutely listed. To verify the capability of real-time processing, several automobile experiments are campaigned with the FMCW SAR sensor on the top of the car. The obtained results of real-time processing and post-processing are presented and compared, processed with 35 cm and 25 cm resolution, respectively.