Various disturbances in voltage source converter based high-voltage, multi-terminal DC grids will significantly cause DC voltage deviations when the classical voltage droop control is adopted. The unsatisfactory voltage deviations weaken the voltage regulation ability and increase the risk of instability. Two flexible controls at the top of the classical voltage droop control to reduce voltage deviations are proposed, and the power–voltage (P–V) curves of the classical voltage droop control are translated co-ordinately. Firstly, a global DC voltage oscillation damping control designed based on the Lyapunov theory is proposed for transient voltage deviations. Secondly, a constant weighted voltage control is designed for reducing steady weighted voltage deviations. The steady active power injections keep almost unchanged under proposed controls, consistent with those under only the classical voltage droop control. The stability influence and the power flow impact are carried out to evaluate the proposed controls theoretically. Tests are conducted on a multi-terminal DC grid with five-terminal voltage source converters. Simulation results show the proposed controls' effectiveness and superiority under various fault conditions, including both the outage of a constant power voltage source converter and a droop voltage source converter.