The lack of inertia and damping mechanism of photovoltaic (PV) grid-connected systems controlled by maximum power point tracking (MPPT) poses a challenge for the safety and stability of the grid. Virtual synchronous generator (VSG) technology has attracted wide attention, since it can make PV grid-connected inverter present the external characteristics of a synchronous generator (SG). Nevertheless, traditional PV-VSG is generally equipped with an energy storage device, which leads to many problems, such as increased costs, space occupation, and post-maintenance. Thus, this paper proposes a two-stage improved PV-VSG control method based on an adaptive-MPPT algorithm. When PV power is adequate, the adaptive-MPPT allows the PV to change the operating point within a stable operation area to actualize system supply-demand, matching in accordance to the load or dispatching power demand; when PV power is insufficient, PV achieves traditional MPPT control to reduce power shortage; simultaneously, improved VSG control prevents the DC bus voltage from falling continuously to ensure its stability. The proposed control approach enables the two-stage PV-VSG to supply power to loads or connect to the grid without adding additional energy storage devices, the effectiveness of which in off-grid and grid-connected modes is demonstrated by typical simulation conditions.