[en] Highlights: • The Cu²⁺ and Zn²⁺ could be efficiently removed in the anaerobic methanation system. • The long-term Cu²⁺ and Zn²⁺ removal could be ascribed to the biological-chemical precipitation. • The removal mechanism of Cu²⁺ differed largely from that of Zn²⁺. Copper and zinc are often used as feed additives and frequently detected in swine wastewater. Anaerobic granular sludge (AnGS) plays an important role in high-rate anaerobic methanation biotechnologies which are widely applied to treat swine wastewater. The removal of Cu²⁺ and Zn²⁺ by AnGS was investigated in the batch and continuous systems. The results of batch experiments showed the adsorption by AnGS could be a significant method for Cu²⁺ and Zn²⁺ removal with efficiencies of 99 % and 49 % respectively. The sulfide precipitation mediated by AnGS could be another significant pathway for Zn²⁺ removal with efficiency of 18–27 % in Protein/M²⁺ experiments and 16–46 % in SO₄²⁻/M²⁺ experiments (M²⁺ represents the total concentration of Cu²⁺ and Zn²⁺). The results of continuous experiment showed, with SO₄²⁻/M²⁺ larger than 1.5, the influent Cu²⁺ and Zn²⁺ could be effectively removed in an anaerobic methanation bioreactor and its effluent Cu²⁺and Zn²⁺concentrations were below 1 mg/L and 2 mg/L separately. The main removal mechanism of Cu²⁺and Zn²⁺ in the anaerobic methanation system was that the biological production of sulfide from sulfate was followed by chemical precipitation and reduction. It is helpful for the removal of Cu²⁺ and Zn²⁺ with organic pollutants simultaneously to eliminate environmental risk of swine wastewater.