The kernel adaptive filters (KAFs) based on the minimum mean square error (MMSE) criterion in reproducing kernel Hilbert space (RKHS) improve the performance of linear adaptive filters but result in instability issues and large burdens of computation and memory in impulsive noises. To this end, a novel Nystrom kernel recursive generalized maximum correntropy (NKRGMC) with probability density rank-based quantization (PRQ) sampling (NKRGMC-PRQ) algorithm is proposed to improve filtering performance, robustness, and computational efficiency of the traditional KAFs in this letter. In a fixed dimensional network structure, the proposed NKRGMC-PRQ algorithm can achieve a comparable performance to KAFs with low computational complexity. Monte Carlo simulations are conducted to validate the superiorities of NKRGMC-PRQ in terms of filtering accuracy, computational complexity, and robustness.