In the paper, with the aid of symbolic computation, we investigate the generalized Hirota–Satsuma coupled KdV system via our Weierstrass semi-rational expansion method presented recently using the rational expansion of Weierstrass elliptic function and its first-order derivative. As a consequence, three families of new Weierstrass elliptic function solutions via Weierstrass elliptic function ℘(ξ;g 2 ,g 3 ) and its first-order derivative ℘′(ξ;g 2 ,g 3 ). Moreover, the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented, and when ξ→∞, these solitary wave solutions approach to some constants.