Abstract: Traditional LMS algorithm not only has simple calculation, but also is easy to implement. But Traditional LMS algorithm has the contradiction between convergence speed and steady-state mean square error in performance. A variable step size least mean square (LMS) algorithm, which is based on hyperbolic tangent function of using norm, has been proposed to solve this problem. During the experiment, the convergence rate, tracking performance, steady-state mean square error and anti-jamming performance has become the four main research aspects, with the help of theoretical analysis and experimental simulation. Also, the novel algorithm is compared with other variable step size LMS algorithm. Simulation results show that the proposed algorithm is superior to other variable step size algorithm during the above aspects, in the case of a high signal-to-noise ratio or low signal-to-noise ratio.