Current-source converters (CSCs) have a promising potential to interface the large-scale photovoltaic (PV) generators to electric grids. In order to overcome several drawbacks associated with the conventional vector-controlled CSC-based PV systems, this paper presents for the first time, the power synchronization control (PSC) scheme for the single-stage grid-connected CSC-based PV generator. A detailed small-signal model for the complete CSC-based PV system with the PSC strategy is developed to investigate the system stability, characterize the converter interactions with the electric grid, and design the controller parameters. The PSC of the CSC-based PV system reflects a stable performance under different operating conditions and following sudden variations in the insolation level. Due to the inherent synchronizing feature of the PSC, the phase-locked loop is eliminated and, hence, the integration to the very weak grids is seamlessly achieved. Although there is no direct control on the injected ac current to the grid, the inherent self-current-limiting feature of the CSC through the modulation of the regulated dc-choke current offers an overcurrent protection. Detailed nonlinear time-domain simulations results validate the theoretical analysis and show the effectiveness of the PSC strategy.