The variable step-size LMS adaptive filtering algorithm adjusts the weights by constructing a step-size factor, so that the algorithm has faster convergence speed and smaller steady-state error. In order to further improve the performance of the algorithm, an improved variable step-size LMS adaptive algorithm based on S function is proposed. By using the curve characteristics of S function, the algorithm obtains the expression of the step-size factor by translation transformation of the function. According to the requirement of controllability and anti-interference ability, controllable parameters and error vector autocorrelation values are introduced to adjust the step-size factor, and the final model is obtained. An analysis is made to the influence of the values of these parameters on the step-size factor and the filtering performance. The simulation results show that, compared with the existing algorithms, the algorithm has better performance on convergence speed, steady-state error and anti-interference ability.