This paper discusses different communication topologies for cooperative distributed control design of a multi-terminal DC (MTDC) network. In the discussed architecture, the objective of the control design is the DC node voltage control of MTDC grids in different topologies. In DC systems, the DC node voltages are the most important measure, which define the system state and power flow. In this paper, each converter corresponds to an agent in cyber layer, and each agent only requires the node information of neighbor agents in addition to its own information. In distributed control fashion, the necessities of having central controller and complex communication are eliminated. The indispensable monitoring and supervisory systems for MTDC grid provide local sensing-communication capability thereby using local information and coordinating the voltage control in a distributed manner make design and implementation of a cooperative control feasible. The performance of the different type of communication topologies are examined on an eight-terminal MTDC system connecting four offshore wind farms to the four independent onshore grids.