In the paper, we search for some analytical solutions for a new (3 + 1)-dimension Boiti-Leon-Manna-Pempinelli (BLMP) equation. Based on the Hirota bilinear method, bilinear neural network framework expands to more than one hidden layer to construct test functions. By using the symbolic computation software Maple, periodic-type I, II, and III solutions of the new (3 + 1)-dimension BLMP equation are obtained. Besides, the evolution and dynamical characteristics of these solutions derived via the appropriate real values are also exhibited.