The range migration of missile borne synthetic apertare radar (SAR) is very difficult to correct using all the conventional imaging algorithms but the back projection algorithm; however, the large computation burden and the low efficiency are the key problems existing in its practical application. To solve the problems, an extended back projection imaging algorithm for the dechirped missile borne SAR is proposed. Firstly, a new signal model is built for the dechirped missile borne SAR, and the range compression is implemented in the range frequency domain. Secondly, the imaging region is divided into several stripes in range direction, and the raw echo data is back projected to each stripe for coherent integration by using the sub-aperture merging and image splitting technique. Finally, the entire SAR image can be obtained by combining the subimages of all the stripes. The validity of the proposed algorithm is demonstrated by the simulated and real SAR datasets. Testing results indicate that the extended algorithm is appropriate for achieving accurate dechirped missile borne SAR image. Moreover, it can be easily parallelized because the stripe imaging is independent of each other, so that can greatly decrease the computation burden, and improve the computation speed. The method introduced in this paper has important theoretical significance in realistic remote sensing, detection and recognition of military targets and precision guide.