Distributed robust voltage/var control (VVC) aims to regulate voltage, which adopts a more flexible control structure to effectively address voltage uncertainty when high proportion of distributed PV is connected to the distribution networks. For the distributed robust VVC, this paper proposes a novel fully distributed optimization algorithm based on the consensus alternating direction method of multipliers (ADMM). Meanwhile, acceleration strategy with restart is applied to enhance the algorithm convergence. In addition, in order to improve the efficiency of optimization, an asynchronous algorithm considering communication delay is proposed. Simulations verify the superiority of distributed algorithm with acceleration strategies, as well as the convergence and robustness of the algorithm in asynchronous form.