This paper proposes a distributed model predictive control (DMPC) scheme for inter-cell and inter-cluster capacitor voltage balancing control of a cascaded H-bridge multilevel static synchronous compensator (STATCOM). The proposed DMPC does not require a central controller to perform these control tasks as they are cooperatively performed by local controllers placed in the STATCOM cells. Three case scenarios are analysed to highlight the features of the proposed control scheme. The results demonstrate that the DMPC scheme is able to manage large communication delays and communication failures.