When a new energy inverter with traditional first-order virtual inertia is connected to a weak power grid, there is an adjustment contradiction between its output active power steady-state and dynamic characteristics. First, the characteristics and problems of the new energy inverter with various improved structural virtual inertia in stand-alone and grid-connected mode are summarized. Then to promote frequency stability, a second-order virtual inertia optimization control strategy is proposed, one which adjusts the positions of the first-order differential compensation link and the first-order inertia link in the outer power loop forward channel of the second-order virtual inertia algorithm. Finally, a 100 kW new energy inverter grid-connected system simulation platform is built to verify the theoretical analysis. Theoretical analysis and simulation show that the proposed algorithm effectively reduces the frequency change rate in the initial response stage and improves system frequency stability while maintaining the active power steady-state characteristics and power oscillation damping ability. This work is supported by the Youth Fund of Natural Science Foundation of Anhui Province (No. 1908085QE208).