As a prevalent grid-forming control strategy, the virtual synchronous generator (VSG) has been extensively utilized in renewable energy integration to impart virtual inertia and damping to the grid recently. Nevertheless, due to the similar behaviors of synchronous generator (SG), the transient and frequency characteristics of VSG-based systems degrade significantly during power grid voltage sags, which may result in an unstable system. Most existing researches focus solely on transient stability or frequency stability. A method developed to simultaneously improve transient and frequency stability has not been proposed yet. This paper proposes a modified VSG control scheme using transient damping to address both transient and frequency stability issues. Finally, the simulations demonstrate the validity of the proposed method in the two distinct grid voltage sag cases.