The voltage stability control of distribution grids is challenged by the nonlinearity, modeling error, and external disturbances. Distributed cooperative disturbance-rejection control is a novel and promising method to improve the voltage stability of distribution grids. First, the the high-dimension model of inverters is converted into the equivalent input-output model. The extended state high gain observer is utilized to estimate the effects of multiple disturbances containing in the equivalent model. Based on Consensus theory, the distributed cooperative control is designed to achieve the voltage stability regulation and disturbance compensation. To ensure the dynamic performance of the distributed controller, an optimal topology selection method is proposed based on the graph theory and network control system. A test system consisting of four inverters is built in PowerFactory to verify the proposed control strategy. The results show that the proposed control strategy can effectively stabilize the voltage under the parameter error and external disturbance.