In this paper, a novel phase-locked loop less (PLL-less) control method for single-phase grid-connected inverters combining Second-Order Generalized Integrator (SOGI) and Conservative Power Theory (CPT) is proposed, which utilizes the CPT homo integral variable and SOGI for phase adjustment, thus replacing PLL for synchronous control of the inverter with the grid. By establishing the impedance model and analyzing the stability of different control strategies, it is shown that the proposed SOGI-CPT-based strategy can effectively improve the stability margin and stability bandwidth of the grid-connected inverter under wide-range grid impedance. Furthermore, the inverter can achieve robust stable operation under strong, weak, and even extremely weak grid conditions, solely by designing the appropriate parameter k of the SOGI-CPT control strategy. The effectiveness and impedance stability performance of the proposed grid-connected control strategy is verified by the simulation and experiments based on a hardware-in-the-loop simulation platform.