A novel predictive current control scheme is designed to solve the problem of optimal control of an active power filter (APF) with LCL filter. The traditional APF controller uses multi-rotation coordinate system transformation and a PI regulator to control the harmonics. In addition, the resonant control scheme is also available. However, both of them have a disadvantage, i.e., the computational burden increases with the growing order of harmonics. In the novel predictive current control scheme, the proportional predictive control, integral predictive control and the damping algorithm are combined to achieve the optimal control of APF under the condition of fixed computational burden, where the integral predictive control can compensate the model error caused by parameter disturbance. Dynamic and static experiments were carried out on an APF experimental platform, and results verified that the proposed novel predictive current control scheme had an excellent control performance under both the steady-state and varying load conditions, and it can also complete the compensation for high-order harmonics.