In this study, a discrete-time robust nonlinear filtering algorithm is proposed to deal with the contaminated Gaussian noise in the measurement, which is based on a robust modification of the derivative-free Kalman filter. By interpreting the Kalman type filter (KTF) as the recursive Bayesian approximation, the innovation is reformulated capitalizing on the Huber's M-estimation methodology. The proposed algorithm achieves not only the robustness of the M-estimation but also the accuracy and flexibility of the derivative-free Kalman filter for the nonlinear problems. The reliability and accuracy of the proposed algorithm are tested in the Univariate Nonstationary Growth Model. (C) 2013 Elsevier Ltd. All rights reserved.