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In the Fast Factorized Back Projection Algorithm [1], the 2D interpolation in the image domain is an essential procedure to obtain a fine resolution image which is achieved point by point. The computational burden is intensive [2]. This paper presents a modified FFBPA for the spotlight SAR imaging. In this algorithm, the coarse sub-images obtained by back projecting the sub-aperture signals to the imaging grids in local polar coordinates are corrected by the shift in the range dimension and the rotation in the angle dimension. And then the sub-images are fused to synthesize the high resolution image. The method is convenient and efficient in practical operation.