Abstract: The linearly constrained minimum variance (LCMV) adaptive algorithm has some deficiencies, including sensitivity to steering vector error and large calculation requirements for the inversion of the covariance matrix. To solve these aforementioned issues, we propose an improved LCMV beamforming algorithm, which uses a variable step-size least mean square (LMS) algorithm to obtain the optimal weight vector. This algorithm avoids the inversion calculation and reduce the influence on the performance the algorithm caused by the fixed iteration step size. The problem with the steering vector direction is solved by using a fourth-order cumulant algorithm. Simulation results indicate that the proposed LMS-LCMV algorithm not only can adaptively estimate the steering vector, but that it also has a faster convergence rate and a smaller steady-state error.