Abstract: In worse impulsive noise environment, the performance of the nonlinear signal prediction of the kernel recursive least square (KRLS) algorithm and kernel recursive maxmum correntropy (KRMC) algorithm is degraded in nonlinear systems. So,the kernel recursive least mean P-norm (KRLMP) algorithm is proposed.Firstly,using kernel method,the input data is mapped to reproducing kernel Hilbert space(RKHS).Secondly,based the least mean P-norm and regularization method, the optimal solution of the adaptive filter is deduced, which reduces the influence of non-Gaussian pulse and the small sample size.Then,using the matrix inversion theory, the recursion formula of the matrix is obtained. Finally, the kernel method is used to calculating the filter output efficiently in the input space and the algorithm is obtained.The simulation results of prediction of a Mackey-Glass time series in alpha-stable distribution noise show that compared with KRLS algorithm and KRMC algorithm, KRLMP has a strong impulsive noise rejection capability and good robustness.