This paper presents a new ED (economic dispatch) algorithm for thermal unit generation scheduling in a power system, which guarantees the near optimal solution without reducing calculation speed. It is well known that the accuracy of the fuel cost function has a great influence on the accuracy of the ED solution. However, a roughly approximated quadratic function of the generation cost has generally been used due to the difficulties in dealing with a cost function reflecting the nonlinearity of the actual generator response. In this paper, a new method is proposed to improve both the accuracy and the calculation speed of the ED. By using the inverse incremental cost functions, the ED can be transformed into a simple optimization problem associated with an n-th order polynomial equation. The proposed method reduces the computation time with adaptability to any higher order generation cost functions. The proposed method is tested with sample systems, which shows that the proposed algorithm yields more accurate and economical results with high computation time.