Abstract: In order to improve recovery accuracy of the greedy algorithms, Bayesian hypothesis Testing Match Pursuit (BTMP) algorithm is proposed. Firstly, this algorithm presents a Bayesian hypothesis testing model which is used to identify the indexes of nonzero elements of sparse signal in the noisy case. Secondly, the output index-set of pursuit algorithm is used as the candidate set of this mode, and then every element of the set is tested to eliminate redundant indexes. Finally, the evaluation of sparse signal is reconstructed from the eliminated indexes set by least-squares algorithm. Simulated results show that in the same conditions, BTMP algorithm has no redundant indexes, and shows better anti-jamming ability and recovery accuracy than those of the traditional greedy algorithms.