Biochar (BC) usually has abundant surface functional groups, well-developed pore structures and high specific surface areas, which can combine with transition metals for peroxymonosulfate (PMS) activation to degrade organics. In this paper, BC modified with Cu/CuO was prepared by a modified impregnation pyrolysis method using peanut shells as raw materials. The morphology, structure and physicochemical properties were analyzed. Results showed that the originally smooth BC surface was modified into a rough structure with distributed metal particles, and the specific surface area of the modified Cu/CuO-BC700 (i.e., Cu/CuO-BC) increased from the initial 22.57 to 192.64 m2/g. The Cu/CuO-BC was employed for PMS activation and tetracycline (TC) degradation, achieving a removal efficiency of 93.2% at TC initial concentration 20 mg/L, PMS concentration 0.5 mM and catalyst dosage 0.1 g/L after 30 min. The influence of co-existing anions in the actual water on TC degradation followed the order of HCO3− > H2PO4− > Cl−, and HA had an inhibitory effect on TC degradation. A variety of active species participated in TC degradation, and the free radical pathway played a dominant role. Furthermore, the Cu/CuO-BC could maintain the degradation efficiency of TC up to 80% even after five consecutive cycles. The Cu/CuO-BC maintained high activity through redox reactions between catalytically generated active species and the cycling of metal ions (Cu+/Cu2+).