This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems, which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using a radial basis function neural network, while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated, while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design, which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given, which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be summarized as follows: 1) an output entropy model is presented using a neural network; 2) a nonlinear filter design algorithm is developed as the main result; and 3) a solution of the entropy assignment problem is obtained, which is an extension of the presented framework.