This paper introduces a robust affine projection algorithm for nonlinear acoustic echo cancellation using simplified Volterra filters. Numerically unstable step of affine projection algorithm, matrix inversion, is improved by approximating the symmetrical matrix with a Toeplitz matrix and applying Levinson-Durbin recursion. Furthermore, the adaptive filter weight update is simplified such that the complexity of the algorithm is comparable to the number of the filter parameters. The simulation results show a slightly better performance than that of the well known normalized LMS algorithm.