Although the traditional LMS algorithm has many advantages, such as simple methods and small burden in computation，but for the sake of constant step, it is always into contradictions in the relationship between solving the steady-state error and convergence. Based on brief discussion of fixed step-size LMS, and the principle of adjusting step-size for variable step-size LMS algorithm, by constructing a nonlinear function between the step factor and the error signal , a new variable step-size LMS algorithm based on sine function is proposed, along with the performance analysis with regard to different parameters. The theoretical analysis and simulation results show that the convergence speed and steady-state error of this algorithm are better than those of the fixed step-size LMS algorithm and SVS-LMS algorithm.