In traditional localization methods for Synthetic Aperture Radar (SAR), the bistatic range sum (BRS) estimation and Doppler centroid estimation (DCE) are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R) pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.