This paper proposes a data-driven and fully distributed volt/var control (VVC) method for active distribution networks (ADNs) with multiple virtual power plants (VPPs), which is model-free and robust against bad data in measurements. The proposed scheme combines the advantages of a robust regression based feedback optimization algorithm and a revised alternating direction multiplier method (ADMM). Each VPP continuously obtains local system feedback to correct control strategies, and exchanges only limited information with its neighbors. Furthermore, faster convergence is achieved by applying Nesterov’s accelerated gradient method to the dual update in ADMM. The effectiveness of the method is demonstrated via numerical simulations using several distribution systems.