The stability and dynamic performance of the grid-connected converter is greatly affected by the coupling between the phase-locked loop (PLL) and the current loop control under weak grid conditions. The traditional control strategies use PLL to obtain the frequency and phase of the grid, which ignore the influence of the PLL and cannot adapt to weak grid conditions. To address this problem, the control and stability of the LCL-Type grid connected converter without PLL under weak grid conditions are studied in-depth in this paper. Firstly, the digital controlled model of the LCL-Type grid-connected converter with capacitor-current feedback active damping is established, and the stability of the system is analyzed. Then, a control strategy without PLL is proposed. The proposed strategy decomposes the grid voltage signal into instantaneous active and instantaneous reactive components through the αβ frame, which can realize the independent control of active and reactive current by simple calculation. The obtained results show that the strategy avoids the influence of the PLL on the inner loop current, and has the advantages of strong stability and anti-interference ability under weak grid conditions. Finally, simulation and experiment results are provided to verify the validity of theoretical analysis.