In this paper, we present the asymptotic “solutions” of the general Heun equation in terms of the orthogonal polynomials with respect to certain perturbed “classical” Jacobi weights. Our approach employs a double limit, which includes changes in variables or scaling. We construct the second-order differential equations satisfied by the orthogonal polynomials generated by the given Jacobi-type weights as an approximation for the general Heun equation.