Unit commitment is an efficient method to lower the total cost of the power plant by scheduling units' generation and meeting the constraint condition. However, in practice, few power plants implement the algorithm for fear that the load response in the power plant would not be fast enough to track the unscheduled load demand from the power grid if some units of the power plant are shut down. This paper proposes a new unit commitment method that tries to solve this problem effectively. The proposed method guarantees the desired speed limit by setting the plant-level load tracking speed. In this method a ‘one-at-a-time’ unit commitment is accomplished. The most expensive unit (which is determined by computing its cost) is optimized, the unit commitment schedule is updated, and the load dispatch result is re-computed. The result will be repeatedly optimized until the spinning reserve or load tracking speed is lack. The optimization loop will breaks out as well if the unit schedules of two consecutive iterations over the time period remain unchanged. The test results from 10-machine system shows that the proposed method is easy to understand and quick to solve, and is of practical use.