In a photovoltaic (PV) power generation system, the grid-connected inverter is directly connected to the power grid. Under the state of grid sub-synchronous oscillation (SSO), the working performance will be interfered with, affecting the stability of the PV power generation system. This paper first establishes the mathematical model of the PV grid-connected inverter under the influence of grid SSO and explores the impact of grid SSO on the control strategy of the PV grid-connected inverter. Secondly, the Prony algorithm is improved, and an adaptive quasi-resonant controller (A-QRC) optimized by the improved Prony algorithm is proposed, thereby eliminating the disturbance effect of SSO on the PV system. Finally, the simulation model of PV generation system oscillation suppression is established to certify the effectiveness of SSO suppression strategy proposed in this paper.