With the help of symbolic calculation software Maple, a new (3+1)-dimensional Boussinesq equation was proved to have consistent tanh integrability. Many interaction solutions among solitons and other types of nonlinear waves, such as simple soliton solution, soliton-cnoidal wave interation solution and resonant soliton solution, were given by selecting different solutions under consistent conditions equation. The corresponding graphs of soliton-cnoidal wave interation solution and resonant soliton solution were presented.