This paper focuses on the modeling and stability analysis of the typical single-phase phase-locked loop (PLL) based on second-order generalized integrator (SOGI). Traditionally, SOGI-based PLL (SOGI-PLL) is linearized as the linear time-invariant (LTI) model for the stability analysis and parameter design. Yet, the PLL has periodical nature due to the periodical variation of the grid voltage. The traditional LTI model for PLL thereby reduces the precision of stability analysis. For addressing this problem, an accurate linear time-periodic (LTP) model of the single-phase SOGI-PLL is proposed in this paper. The proposed model can precisely characterize the coupling nature of phase, frequency, and amplitude estimated by SOGI-PLL. A precise stability region of SOGI-PLL thereby can be derived from the proposed LTP model. The effectiveness of the proposed LTP model for SOGI-PLL is verified by simulation and experimental tests.