In this paper, an efficient nonlinear echo cancellation method is proposed, whereby the fast block exact Gauss-Seidel pseudo affine projection (FBEGS-PAP) is further utilized for adaptive Volterra filtering. In particular, the proposed nonlinear echo cancellation approach requires lower computational complexity as in the conventional linear adaptive echo cancellation methods based on NLMS and GS-PAP, and still provides nonlinear echo cancellation performance similar to the GS-PAP method. Finally, echo cancellation performance of the proposed approach is demonstrated by providing some simulation results.