Summary: The modified unstable nonlinear Schrödinger equation is first reduced to a system of second-order nonlinear partial differential equations, then some nonlinear algebraic equations and nonlinear ordinary differential equations are obtained by choosing different parameters. Some explicit and exact solutions of nonlinear ordinary differential equations, which are reduced by a kind of combination of a direct method and ansatz method are found. Thus explicit and exact solutions for the modified unstable nonlinear Schrödinger equation are obtained. These solutions include the exact plane wave solutions, solitary wave solutions of the bell-shape, solitary wave solutions of the kink-shape, the singular travelling wave solutions, and periodic wave solutions of triangle function.