In this work, a new generalized Jacobi elliptic function rational expansion method is based upon twenty-four Jacobi elliptic functions and eight double periodic Weierstrass elliptic functions, which solve the elliptic equation ϕ′ 2= r+ p ϕ 2+ q ϕ 4, is described. As a consequence abundant new Jacobi–Weierstrass double periodic elliptic functions solutions for (3+ 1)-dimensional Kadmtsev–Petviashvili (KP) equation are obtained by using this method. We show that the new method can be also used to solve other nonlinear partial differential equations (NPDEs) in mathematical physics.