Many travelling wave solutions of nonlinear evolution differential equations can be written as a polynomial of two elementary functions which satisfy a projective Riccati equation. From that property, we deduce a method for building these solutions by establishing the relation between the solutions of the general elliptic equation and the projective Riccati equation. The method is effective for both type Ⅰ and type Ⅱ equtions. At the same time, we also answer the question of how to construct the elliptic function solutions in fraction form to the nonlinear evolution equations.