With the increasing penetration of renewable energy and the increasing uncertainty, the reactive power optimization of islanded microgrids face increasingly severe challenges. According to the topological structure of the meshed islanded microgrids, the power flow model is convex into a two order cone power flow model. Considering the uncertainties of PV active power and PV inverter reactive power, we establish an adjustable robust reactive power optimization model. Based on the strong duality theorem, the uncertainties in the robust model are eliminated and solved by linear robust optimization. Finally, we use the IEEE 33-bus system to simulated and tested reactive power optimization model which propose in this paper. The results show the robust optimization model still has good robustness after reducing the conservatism. It can ensure the stable operation of the system.