This paper presents a new solution method to efficiently handle non-convexity stemmed from valve points in the economic Load dispatch problem. The proposed solution technique integrates both the advantage of fast solution algorithms of linear programming and powerful solution techniques of nonlinear programming to find the global solution. In the first step of the proposed solution framework, non-convex terms are replaced by some linear segments and the new linear model solved by modern fast algorithms. In the second step, a nonlinear programming algorithm as a powerful local search algorithm solves the original non-convex model to improve the solution obtained in the previous step. By exploiting the main strength of linear and nonlinear programming algorithms, the proposed solution approach can quickly converge to nearly the global solution method. By experimental results on three test cases with different sizes, we show that the presented method outperforms the other algorithms published in the literature in the quality of the solution.