Keeping the synchronization of a grid feeding converter (GFC) with a weak grid during deep voltage sags has been introduced as a serious challenge in converter-interfaced renewable energy source-dominated weak grids. To deal with this challenge, a simple yet effective solution based on the virtual inertia concept is proposed in this article. This method is realized by adding a correction term to the dc-link voltage controller, which adjusts the active and reactive current set points and enables the converter to remain synchronized to the grid during severe faults. Closed-loop dynamics of the system in the presence of the parametric uncertainty of the grid-side impedance has been studied, in both normal and fault conditions with different voltage drops. Along these, system performance has been investigated, and in comparison with previous methods, it is revealed that the direct inertial support gain may possibly cause instability and do not propose a stable synchronization process to the GFC under deep faults. The performance of the proposed method has been verified by real-time laboratory results for different resistive/inductive weak grids with various levels of voltage sags. Real-time verification demonstrates the effectiveness of the proposed control in stabilizing GFCs for inertia emulation and its role in a better synchrony process.