Abstract: IIn the field of signal processing, the traditional adaptive filtering algorithm with fixed step size cannot take the steady-state error and the convergence speed into account at the same time. To solve this problem, the least mean p-norm (LMP) algorithm needs to be improved, and an improved variable step size least mean p-norm (IVSLMP) algorithm based on the improved hyperbolic tangent function is proposed. The algorithm uses an improved hyperbolic tangent function to adjust the step size, and uses a moving weighted average method to construct a variable step function; at the same time, an adjustment function is introduced to further improve the performance of the algorithm. Through the simulation experiment under the interference of ocean impulse noise, it is shown that compared with the existing fixed step size and variable step size algorithms, the improved variable step size LMP algorithm can well take the convergence speed and steady state error of the system into account; and for the new algorithm after introducing the adjustment function, the steady state error is further reduced while ensuring the convergence speed of the original algorithm, so that the convergence and stability of the algorithm are better considered, and it has better feasibility.