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Multiple sound source localization remains a challenging issue due to the interaction between sources. Although traditional approaches can locate multiple sources effectively, most of them require the number of sound sources as a priori knowledge. However, the number of sound sources is generally unknown in practical applications. To overcome this problem, a spatial principal eigenvector based approach is proposed to estimate the number and the direction of arrivals (DOAs) of multiple speech sources. Firstly, a time-frequency (TF) bin weighting scheme is utilized to select the TF bins dominated by single source. Then, for these selected bins, the spatial principal eigenvectors are extracted to construct a contribution function which is used to simultaneously estimate the number of sources and corresponding coarse DOAs. Finally, the coarse DOA estimations are refined by iteratively optimizing the assignment of selected TF bins to each source. Experimental results validate that the proposed approach yields favorable performance for multiple sound source counting and localization in the environment with different levels of noise and reverberation.