Abstract: In practical communication situations,the performance of linearly constrained least squares constant modulus algorithm(LSCMA) is known to degrade severely in the presence of even slight signal steering vector mismatches.In view of this problem,a novel robust constrained LSCMA based on Bayesian approach is proposed.The proposed algorithm estimates direction of arrival(DOA) of the actual signal from the observed data and priori knowledge about the source DOA.The iterative formula of the weight vector is derived by the norm constraint condition.The proposed algorithm provides excellent robustness against deviation of DOA,thus the uncertainty in the DOA of the actual signal is reduced,and the algorithm makes the output array SINR close to the optimal value.The proposed robust adaptive beamforming algorithm can reduce the computational complexity for using the recursive method to obtain inverse matrix and be implemented in real-time situations.Computer simulation results demonstrate that the proposed algorithm can outperform linearly constrained LSCMA in the complex communication environment.