In this study, anaerobic granular sludge with sulphate-reducing bacteria (SRB) was applied to treat Cu2+-, SO4(2-) -containing wastewater in an expanded granular sludge bed reactor. The migration and enrichment of copper in anaerobic granular sludge were envaluated. By analysing the sludge with X-ray diffraction, copper was determined to be present as covellite (CuS) in the sludge. Observations at the microscopic level showed that CuS precipitates were absorbed onto granules and gradually migrated from the outer to the interior layer of the granule over time and finally accumulated in the core of the granular sludge. Because of the migration of the CuS precipitates and the protection of the extracellular polymeric substances matrix, SRB were able to tolerate copper concentrations up to 10 mg/L. A copper removal efficiency of about 96% was observed at a steady state for 3 months, and copper was enriched in the granular sludge.