In the paper, a new expansion auxiliary equation method is proposed. By this method, traveling wave solutions of the simplified MCH equation and the ZKBBM equation are constructed successfully, including soliton solutions, singular solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic solutions and other new solutions, their characteristics are demonstrated by three-dimension and two-dimension profile figures and comparisons with previous references are made. It is shown that our proposed method can obtain new and more general solutions of nonlinear evolution equations and would be a powerful mathematical tool for solving nonlinear evolution equations.