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Power utilities in general use Lagrangian method to solve economic dispatch (ED) problem for ease of implementation. This is possible only if the cost function of generating units is convex. Owing to valve-point effect exhibited by multi-valve steam turbines, the cost function is non-convex. The Maclaurin series-based Lagrangian method is proposed to solve complicated, non-convex and non-linear ED problems. In this method, the rectified sinusoid function is represented by Maclaurin sine series expansion and is solved using the Lagrangian method. The problem is solved iteratively using lambda iteration method. The proposed methodology is validated using IEEE 30-bus test system. In addition, the effectiveness of the new algorithm is demonstrated with 3, 13 and 40 generator test systems available in the literature. The results obtained substantiate the applicability of the proposed method for solving ED problems with non-smooth cost functions at par with stochastic search techniques generally used.