Static voltage stability margin (SVSM) is a commonly used voltage stability evaluation index in power system operation. The SVSM will change with the uncertain fluctuation of wind farm output, which may threaten the secure operation of a power system. Therefore, this paper proposes an optimal control model for the SVS of an AC/DC hybrid power grid considering the uncertainty of wind farm output. With the objective of minimizing the total control cost, it is required that the lower bound of the system SVSM fluctuation range meets the predefined safe operation requirements under a given fluctuation range of wind power output. In order to solve the three?layer optimization model, a parametric approximation method is introduced, and the inner and middle layer optimization models are parameterized layer by layer, which helps to obtain the approximate analytical expression of the relationship between the lower bound of the SVSM interval and each control variable. The optimization model is converted into a single?layer optimization model, and the SBB solver is used to obtain the optimal control scheme. Meanwhile, to improve the computational efficiency, a method of removing redundant cross terms in the approximate polynomials is proposed by using high?order mixed derivatives of SVSM with respect to control variables. Finally, a modified IEEE 39?bus AC?DC hybrid system is used as an example to verify the correctness and effectiveness of the proposed method.