The auxiliary equation method proposed by Sirendaoreji is extended to construct new types of elliptic function solutions of nonlinear evolution equations. The effectiveness of the extended method is demonstrated by applications to the RKL model, the generalized derivative NLS equation and the Kundu-Eckhaus equation. Not only are the Jacobian elliptic function solutions are derived, but also the solitary wave solutions and trigonometric function solutions are obtained in a unified way.