In an LCL grid-connected inverter system, there is a big contradiction between adjusting the closed-loop structure to meet system performance and ensuring the internal stability of the system. To solve this problem, a grid-connected current control method based on a parameterized stabilization controller and H2 norm of the error signal is proposed. This method uses the parameterized stabilization controller to ensure the internal stability of the system, and then determines the free parameters of the stabilization controller and open-loop gain coefficient by designing the H2 norm of the error signal and open-loop gain, so that the system has a fast dynamic response and zero steady-state error. This method can not only greatly suppress the interference of the grid voltage on the grid current, but also the grid-connected inverter system can quickly and accurately output the three-phase balanced sinusoidal current within half a cycle when the reference current changes suddenly under different operating conditions. The performance and validity of the proposed control scheme are verified by simulations and experimental results. This work is supported by the National Natural Science Foundation of China (No. 51577162).