There is a problem of the reduction of inertia and frequency stability caused by the high penetration of renewable power in a power system. Thus it is necessary to explore and enhance the frequency regulation capability of synchronous generators. Considering the different frequency support capability of the synchronous generators in a power system, the effect of adjustment coefficient of different units on the maximum frequency deviation is analyzed based on sensitivity analysis. The expression of maximum frequency deviation is derived considering the frequency regulation capability of both the synchronous generators and wind power. This paper proposes a multi-objective frequency constraint unit commitment model considering the sensitivity of the synchronous generator adjustment coefficient. Non-dominated sorting genetic algorithms-II (NSGA-II) are introduced to analyze this model. Simulation results show that the proposed unit commitment model enhances the frequency regulation capability of the synchronous generators, increases the minimum frequency, and improves the frequency stability of the power system.