The orthogonal matching pursuit (OMP) algorithm must set a redundant su pport in advance,which leads to heavier computation burden,lower noise suppressi ve ability and poor signal reconstructed p erformance.This paper proposes a Bayesian orthogonal matching pursuit(BOMP) algorithm.Firstly,the redundant support is properly del eted by using Bayesian model and OMP algorithm to obtain a proper support,which is equivalent to the real support or so. Secondly,the BOMP sparse signal reconstruction algo rithm is constructed.Finally,the BOMP algorithm is used for ISAR imaging.Simul ation results and experimental results of real data show that by means of approximate estimation of sparsity,the proposed algorithm can enhance the noise suppressive ability,recon struction accuracy and decrease the computing complexity obviously.