We propose a new robust recursive fixed-interval smoother for nonlinear systems under non-Gaussian process and measurement noises, i.e., the nominal Gaussian noise is polluted by large noise from unknown distributions. Taking advantage of correntropy in handling non-Gaussian noise, a robust Rauch-Tung-Striebel smoother is derived according to the maximum-correntropy-criterion-based cost functions with nonlinear functions linearized by their first-order Taylor series expansions, where two weights are utilized to adjust the estimation gains of forward filtering and backward smoothing, respectively. Simulation results demonstrate the effectiveness of the proposed smoother in the presence of various non-Gaussian process and measurement noises, especially the shot sequences and multimodal noise.