Abstract: In order to improve the performance of nonlinear channel equalizer for α-stable noise, combining with the core thought of the least mean p-norm (LMP) algorithm, the paper took advantage of the kernel method to deal with nonlinear problems and constructed the nonlinear equalizer which is based on kernel method for α-stable noise. At the same time, the kernel least mean p-norm (KLMP) algorithm was produced and inferred in this paper. First of all, received signal was mapped into the high dimensional feature spaces by kernel function; Then, the LMP algorithm was employed to equalize signal in the high dimensional feature spaces; In the end, output signal of the equalizer in the high dimensional feature spaces was expressed in inner product and turned into input spaces by kernel function to compute. Theoretical analysis and simulation results show that the new algorithm decreases the steadystate error on the condition that the convergence rate is guaranteed and can better compensate nonlinear channel distortion when compared with the kernel least mean square (KLMS) algorithm and the LMP algorithm.