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In this paper, based on a system of the first order differential equations with three nonlinear ordinary differential equations (ODEs), a new tri-function method is presented to investigate exact solutions of a wide class of nonlinear wave equations. The method is constructive and can be carried out in a computer with the aid of symbolic computation. In particular, we apply the tri-function method to the (3 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and the (2 + 1)-dimensional nonlinear Schrodinger (NLS) equation such that many types of new exact solutions are obtained, which contain doubly periodic solutions and solitary wave solutions.