Renewable energy generation and nonlinear load devices will generate harmonics and reactive power to power grids, resulting in current distortion and low power factors. To solve the power quality problems, the LC-coupling hybrid active power filter (LC-HAPF) is proposed, with lower DC-link voltage and lower cost compared with conventional active power filters (APFs). The LC-HAPF requires a controller to operate, therefore, hysteresis current control (HCC) and proportional current control (PCC) were proposed. However, they both result in significant steady-state error. Hence, linear quadratic regulator control (LQRC) with integral action (LQRIC) is proposed for the LC-HAPF in this paper to mitigate the steady-state error. The d-q-0 coordinate state-space model of the LQRIC-controlled LC-HAPF is derived, and a detailed design guideline of the weighting matrices Q and R of LQRIC is given. By the state-space model and weighting matrices, the gain matrix K of LQRIC can be acquired by MATLAB, thus a good steady-state performance can be ensured. Finally, the simulation results of different controllers for the LC-HAPF under 40V and 50V DC-link voltages are given to verify the effectiveness of the proposed LQRIC. The experimental results of LQRIC-controlled LC-HAPF are also given to verify the feasibility of the proposed LQRIC.