Abstract: Aiming at the problem that the fixed-step least mean square (LMS) algorithm could not meet the requirements of low steady-state error and fast convergence speed at the same time, a variable-step LMS algorithm was proposed based on the inverse hyperbolic tangent function. Utilizing the inverse hyperbolic tangent function, the algorithm was arranged to construct the non-linear function relationship between the step size and the error signal, so as to replace the fixed step size in the LMS algorithm and realize the dynamic adjustment of the step size factor. In this paper, the influence of the parameters <i<α</i<, <i<β</i< and <i<γ</i< in the new variable step size function on the performance of the algorithm was discussed in detail, and the performance of the algorithm was compared with several other newer variable step size algorithms. The simulation results show that the proposed algorithm takes into account the contradiction among convergence speed, steady-state error and tracking performance, and present excellent performance in system identification, sinusoidal signal denoising and adaptive linear prediction.