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As renewable energy increasingly penetrates into power grid systems, new challenges arise for system operators to keep the systems reliable under uncertain circumstances, while ensuring high utilization of renewable energy. With the naturally intermittent renewable energy, such as wind energy, playing more important roles, system robustness becomes a must. In this paper, we propose a robust optimization approach to accommodate wind output uncertainty, with the objective of providing a robust unit commitment schedule for the thermal generators in the day-ahead market that minimizes the total cost under the worst wind power output scenario. Robust optimization models the randomness using an uncertainty set which includes the worst-case scenario, and protects this scenario under the minimal increment of costs. In our approach, the power system will be more reliable because the worst-case scenario has been considered. In addition, we introduce a variable to control the conservatism of our model, by which we can avoid over-protection. By considering pumped-storage units, the total cost is reduced significantly.