The rapid development of economy and society stimulates the increase of power demand. Wind power has received great attention as a typical renewable energy, and the share of wind power is continually increasing in recent years. However, the high integration of wind power brings challenges to the secure and reliable operation of power grid due to the intermittent characteristic of wind power. In order to solve the operation risk caused by wind power uncertainty, this paper proposes to solve the problem of stochastic security-constrained unit commitment (SCUC) by considering the extreme scenarios of wind power output. Firstly, assuming that the probability density distribution of wind power approximately follows a normal distribution, a great number of scenarios are generated by Monte Carlo (MC) simulation method to capture the stochastic nature of wind power output. Then, the clustering by fast search and find of density peaks (CSFDP) is utilized to separate the generated scenarios into three types: extreme, normal and typical scenarios. The extreme scenarios are identified to determine the on/off statuses of generators, while the typical scenarios are used to solve the day-ahead security-constrained economic dispatch (SCED) problem. The advantage of the proposed method is to ensure the robustness of SCUC solution while reducing the conservativeness of the solution as much as possible. The effectiveness of the proposed method is verified by IEEE test systems.