Abstract: The problem of step size selection for adaptive least mean squares(LMS) filtering algorithm is studied.A new variable step size LMS algorithm with improved hyperbolic tangent function is presented,which is derived by the extensive review about some existing LMS algorithms.The selective rule of step size parameters is discussed,and the performance analysis such as convergence,anti-interference and the steady-state error of the algorithm are also given.The algorithm can not only obtain the good properties of the fast convergence and the tracking speed,but also achieve lower misadjustment.Theoretical analysis and simulation results show that the proposed variable step size LMS algorithm has better steady-state performance than that of the existing algorithms.