In order to improve the adaptability of the grid-connected inverter under the unbalanced and harmonic voltage condition and make it produce high quality grid-connected current, it is necessary to improve the traditional grid-connected inverter control strategy. This paper focuses on the model of LCL grid connected inverter in a αβ coordinate system, and presents a control strategy of Quasi Proportional Resonant (QPR) and grid voltage feedforward. Firstly, the paper analyzes the relationship between the grid-connected current and its given value & grid voltage to get the reason why the steady-state error and disturbance component perturbation component produced. Then, a QPR control strategy is introduced to realize the zero-steady-state error control of grid-connected current and the voltage feedforward control is added to suppress the direct effect of grid disturbance on grid-connected current. At the same time, an improved phase-locked loop control strategy is also introduced to improve the accuracy and the ability of harmonic suppression of traditional one under non-ideal grid voltage state, thereby enhancing phase-locked loop anti-interference. Finally, the simulation results based on Matlab/Simulink show that the proposed control strategy not only gets high-quality grid-connected current under the status of unbalanced and harmonic grid voltage, but also ensures the efficient and stable operation of the inverter, verifying its validity and correctness.