Abstract: In the model predictive current control of grid connected inverter with an inductive-capacitive-inductive (LCL) filter, the digital delay will introduce control error, and the accuracy of the plant model may also affect the predictive control performance. In order to reduce the impact of digital delay and the sensitivity of predictive control to system model changes, and enhance the output performance of grid connected inverter with LCL filter in the weak grid, a deadbeat predictive current control strategy based on disturbance compensation is proposed. The improved deadbeat predictive control strategy based on linear interpolation is adopted to reduce the control error caused by digital delay. Based on the impedance identification of weak grid, the internal model disturbance observer is designed. The adaptive gain satisfying the stability of the system is selected by constructing Lyapunov function, so as to suppress the influence of disturbance such as model mismatch and measurement noise on the predictive control performance, and thus improve the adaptability of the inverter in weak grid. Finally, theory analysis, simulation, and experimental results are presented to illustrate the effectiveness of the proposed control techniques.