Scheduling the economic generation of thermal units is a critical task in a large-scale power system because it significantly reduces annual production cost. This study presents a novel double-filtration algorithm to solve the problem of combining unit commitment and economic dispatch of the thermal units while minimizing cost. The proposed algorithm first uses two strategies and a redundancy factor to divide all of the units into five groups and find potential combinations. Then it employs an immature economic dispatch method and a look-forward rule to obtain the optimal unit scheduling. Moreover, a conventional economic dispatch method and a look-backward rule are applied to find the actual solution. Finally, two test cases are simulated and the results are compared with existing methods. Simulation results demonstrate the outstanding performance of the proposed method.