Active power filter(APF) is the most popular device in regulating power quality issues. Commonly, a APF controlled current by detected reference current and then tracked the reference current. However, the reference current detection sustain a large amount of computation, in addition, existing error and delay, which effect the dynamic and steady compensation performance of APF. In other hand, a optimal control is based on precise model. However, most literatures modeling in APF singly and rarely considering the impact of grid impedance and load impedance, let alone considering the impact of nonlinear load. Thus this paper established a model consist of LC APF, load and grid impedance, which included disturbance of source voltage and load harmonics current. And then applied linear quadratic regulator(LQR) optimal control in inner current loop design without reference current detection and active damping. Analyzed the effect of grid impedance and load impedance by Bode diagram. At last, compare proposed algorithm with conventional control algorithm. Verified the established model and control algorithm in MATLAB/Simulink and LC APF prototype. The results prove that the established model is correct and the proposed algorithm response fast, compensation harmonics well and is robust in a wide range of parameter variations.