The continuous increasing share of power-converter-based renewable energies weakens the power system inertia. The lack of inertia becomes a main challenge to small-scale modern power systems in terms of control and stability. To alleviate adverse effects from inertia reductions, e.g., undesirable load shedding and cascading failures, three-phase grid-connected power converters should provide virtual inertia upon system demands. This can be achieved by directly linking the grid frequency and voltage references of dc-link capacitors/ultracapacitors. This paper reveals that the virtual inertia control may possibly induce instabilities to the power converters under weak grid conditions, which is caused by the coupling between the d- and q-axes as well as the inherent differential operator introduced by the virtual inertia control. To tackle this instability issue, this paper proposes a modified virtual inertia control to mitigate the differential effect, and thus, alleviating the coupling effect to a great extent. Experimental verifications are provided, which demonstrate the effectiveness of the proposed control in stabilizing three-phase grid-connected power converters for inertia emulation even when connected to the weak grid.