As a high-quality imaging method for non-linear motion SAR, back projection (BP) algorithm's huge computational cost hinders its applications. In recent years, the emergence of GPU as a high-performance computing platform counteracts this disadvantage greatly, and brings the BP algorithm into people's perspective. In accord with the SAR's working procedures, the streaming structure is suitable for massive SAR data processing. Thus, a streaming BP algorithm and a piecewise high-order polynomial fitting method for IMU data preprocessing that is compatible to the streaming structure are proposed in this paper. The validity and performances of the fitting method are verified and discussed using actual IMU data. We find that the 9th-order polynomial fitting can meet the requirement of typical actual IMU data processing. The validity of the streaming BP for non-linear motion compensation is verified via actual SAR data, and its computing performance is analyzed and optimized on NVidia's GTX 590. The total runtime of the streaming BP on the GPU platform for an image with size 8192x8192 pixels is about 160 s, which can meet the requirements of many off-line SAR imaging applications.