A greedy algorithm called Bayesian multiple matching pursuit (BMMP) is proposed to estimate a sparse signal vector and its support given $m$ linear measurements. Unlike the maximum a posteriori (MAP) support detection, which was proposed by Lee to estimate the support by selecting an index with the maximum likelihood ratio of the correlation given by a normalized version of the orthogonal matching pursuit (OMP), the proposed method uses the correlation given by the matching pursuit proposed by Davies and Eldar. BMMP exploits the diversity gain to estimate the support by considering multiple support candidates, each of which is obtained by iteratively selecting an index set with a size different for each candidate. In particular, BMMP considers an extended support estimate whose maximal size is $m$ in the process to obtain each of the support candidates. It is observed that BMMP outperforms other state-of-the-art methods and approaches the ideal limit of the signal sparsity in our simulation setting.