A finite-set model predictive control (FS-MPC) with coupling capacitor voltage observer scheme is proposed for thyristor-controlled LC-coupling hybrid active power filter (TCLC-HAPF) in this paper. It ensures the fast transient response, low steady-state error and good robustness under both inductive and capacitive load situations. Generally, the implementation of FS-MPC for TCLC-HAPF requires sensing of coupling capacitor voltage and thyristor-controlled reactor current in addition to sensing load voltage, load current and compensation current, which increases the system complexity and cost. To relax this problem, the simplified predictive model is first proposed, thus reduce the required sensing signals and system order. Then, a coupling capacitor voltage observer is utilized to reduce the hardware costs, which can obtain a comparable performance with directly sensed capacitor voltage. The delay compensation is also considered for the control delay in practical realization. Finally, the effectiveness and performance of the FS-MPC with coupling capacitor voltage observer for TCLC-HAPF are verified by simulated and experimental results.