It is a challenging task to design controller for the digitally controlled LCL-filtered grid-connected inverter to achieve high-quality grid current, avoid undesired resonance, and offer robust performance against system parameters uncertainties. To address the problem, in this study, the linear quadratic regulator (LQR) for a digitally controlled grid-connected inverter is proposed. Discrete-time state-space model of the inverter is established by discretising the system continuous state-space equations and taking into account one sampling period delay. Then, a systematic design procedure for selecting the state weighting matrix Q is presented, so that the poles of the closed-loop system are assigned and the desired performances can be achieved. Moreover, to further attenuate the grid voltage background harmonics, the selective harmonic controllers are designed based on the LQR. Compared with the conventional dual current loop control strategy, the proposed LQR controller can achieve low harmonic distortion, fast dynamic response, and good robustness against system parameters deviations. Finally, time-domain simulations are carried out in MATLAB/SIMULINK software and experimental tests are performed on the experimental setup. The results have demonstrated the effectiveness of the proposed LQR method.