Constructing exact solutions of cubic nonlinear Schrodinger equation is helpful to understand the relevant physical background of the equation. Some exact solutions of cubic nonlinear Schrodinger equation, such as hyperbolic function solutions, trigonometric function solutions and rational function solutions, are obtained by using the generalized exp［－φ(ξ)］-expansion method and symbolic computation system-Maple. These new solutions contribute to the application in optical communications. It can be seen that this expansion method is very effective for solving nonlinear partial differential equations in mathematical physics problems.