Assuming that there exists an electricity spot market, the contract between one wind power plant and one power grid company is studied. To effectively manage the fluctuation of the wind power supply, both the fixed supply contract and the forecast-commitment supply contract, where the latter transfers part of the supply fluctuation risk from the wind power plant to the power grid company, are studied; this reduces the dependence of the wind power plant on the electricity spot market. The optimal decisions of the wind power plant and the power grid company, as well as the sensitivity of the optimal decisions and profits to the spot market price and the risk attitudes are discussed. Finally, how the government subsidy policy affects the members’ decisions is analyzed and the conclusion is that to provide the subsidy to the wind power plant is always better and a Pareto improvment from the perspective of social welfare maximization. Providing the subsidy to the wind power plant can reduce the rate of the abandoning wind, and increase the dependence of the wind power plant on the electricity spot market.