This paper modifies the virtual inertia control of a grid connected converter and proposes a hybrid control technique to control a grid connected converter under grid unbalanced conditions. To limit fault currents and support fault ride-through, the control technique is changed from the virtual inertia control to the conventional current control during grid unbalances. With the mitigation of the grid unbalance the control is changed back to the virtual inertia control. The paper analyzes the advantages of doing so and introduces a control scheme to achieve the proposed transfer. Simulation results are presented to evaluate the proposed control.