Recently, the passive synthetic aperture (PSA) technique has been used in passive localization to improve the position accuracy of single source by estimating the Doppler parameter of the received signal. However, in the presence of multiple sources, time-frequency aliasing will lead to serious cross-term interference during Doppler signal extraction, resulting in low localization performance. To solve this problem, a spaceborne passive synthetic aperture localization algorithm based on the multiple-stay detector HOUGH transform (MSD-HOUGH) is proposed in this paper. Firstly, an improved convolutional neural network based on the adaptive histogram equalization method (AHE-CNN) is proposed to achieve source number estimation. Then, the PSA Doppler equations are established in the HOUGH domain, which can suppress the cross-term interference of the multiple emitters. Meanwhile, a multiple-stay detector (MSD) is designed to reduce the pseudo-peaks in HOUGH domain. The estimated source number determines when the MSD will be terminated. Finally, a PSA cost function is established based on the estimated Doppler parameter to achieve signal source localization. Experimental results show that compared with other localization methods, the proposed algorithm has a significant improvement for multiple signal source localization.