With the increasing penetration of wind power, its uncertainty has occasioned a serious impact on the safe and stable operation of a power system. Reactive power optimal dispatch of a wind power system is a nonlinear mixed integer programming problem. While satisfying multiple constraints, the optimal value of reactive power control parameters is determined to optimize a specific objective function. A multi-objective reactive power stochastic optimal dispatching model for a power system considering wind power and load uncertainties is established. Two objective functions, i.e. active power loss minimization and voltage stability index minimization, are set up. The multi-objective optimization model is solved by the method of ε-constrained optimization, and the optimal compromise solution is selected by the method of fuzzy satisfaction degree. Two different cases are designed for simulation on the IEEE-57 bus system. The simulation results show that the proposed model and method can effectively solve the reactive power optimal dispatching problem of a power system with wind power, significantly reduce the active power loss and improve the system voltage stability. This work is supported by Key Research and Development Program of Hunan Province (No. 2017GK2241) and Scientific Research Program of Hunan Education Department (No. 19C1194).