An adaptive regularized affine projection (AR-AP) algorithm has recently been proposed in order to achieve good misalignment performance. However, the algorithm requires high computational complexity. To overcome this problem, we propose an adaptive regularized pseudo affine projection (AR-PAP) algorithm. Additionally, we derive the lower bound of the regularization parameter in order to guarantee the stability of the AR-PAP algorithm. Simulation results show that the performance of the proposed algorithm is better than that of the AR-AP algorithm despite its significantly lower complexity.