A centralized secondary control is utilized in a DC islanded microgrid to fine-tune voltage levels following the implementation of droop control. This is done to avoid conflicts between current allocation and voltage adjustments. However, because it introduces a single point of failure, a distributed secondary control is preferred. This paper introduces a consensus-based secondary distributed control approach to restore critical bus voltages to their nominal values and properly distribute current among converters. The critical bus takes the lead in voltage adjustments, with only connected energy resources contributing to regulation. The microgrid is represented as an undirected graph to facilitate consensus building. Two adjustment terms, δv and δi, are generated to assist in returning voltage to its nominal level and correctly allocating current among energy resources. To enhance consistency and improve controller performance compared to those reported in existing literature, all buses are connected to a leader node. In the event of the failure of all converters except one, voltage can still be effectively restored. MATLAB-Simulink simulations are conducted on two medium-voltage DC (MVDC) microgrids to validate the efficiency of the proposed control method. The results confirmed that the proposed control method can effectively maintain voltage stability and enhance the precise distribution of current among agents by 8%.