To improve the performance and meet the regulation demands of multiple operation modes (grid-connected mode and stand-alone mode) simultaneously for the grid-connected inverter, a novel improved control strategy based on droop control and virtual synchronous generator (VSG) control combined with double adaptive coefficients is proposed. It can flexibly adjust the inertia and damping to meet the regulation requirements of different modes. The designed double adaptive coefficients include adaptive coordination coefficients and adaptive inertia coefficients. The former can improve the system dynamic characteristics and enhance the applicability. The latter can further improve the power overshoot and oscillation problems to completely eliminate power overshoot. The power response of the proposed improved control strategy is no overshoot and oscillation, and it can provide inertia and damping characteristics close to the VSG control and has a faster response speed. It can satisfy the power regulation demands in grid-connected mode and the frequency regulation demands in stand-alone mode simultaneously, and has greater applicability and better dynamic characteristics. Finally, the effectiveness and feasibility of the proposed improved control strategy are demonstrated by control hardware-in-loop (CHIL) experiments.