It is well known that most classical test functions to solve nonlinear partial differential equations can be constructed via single hidden layer neural network model by using Bilinear Neural Network Method (BNNM). In this paper, the neural network model of test function for the (3+1)-dimensional Jimbo–Miwa equation is extended to the “4-2-3” model. By giving some specific activation functions, new test function is constructed to obtain analytical solutions of the (3+1)-dimensional Jimbo–Miwa equation. Rogue wave solutions and the bright and dark solitons are obtained by giving some specific parameters. Via curve plots, three-dimensional plots, contour plots and density plots, dynamical characteristics of these waves are exhibited.