In this work, we employ the Jacobi elliptic function method for a reliable treatment on a nonlinear system. We find the exact solutions of a well-known model, namely, Drinfeld-Sokolov (DS) system. The different Jacobi function expansions may lead to new Jacobi doubly periodic wave solutions, triangular periodic solutions and soliton solutions. In addition, as an illustrative sample, the properties for the Jacobi doubly periodic wave solutions of the nonlinear equations are shown with some figures.