Grouper (Epinephelus malabaricus) were fed five diets, which were supplemented 0, 5, 13, 24 and 41 mg copper (Cu)/kg diet for 6 weeks, and changes in growth performance, RNA/DNA ratio, digestive enzyme activities and oxidative stress were investigated. The result showed that weight gain rate (WGR) and specific growth rate (SGR) increased with increasing dietary Cu concentrations, and concentration-dependent decrease was observed in feed conversion rate (FCR). Cu concentration-related increase in RNA: DNA ratio was observed in white muscle. Hepatosomatic (HIS) and viscerosomatic index (VSI) were not affected by the dietary Cu supplementation (P > 0.05), and protein efficiency ratio (PER) and condition factor (CF) were stimulated in a Cu concentration-dependent manner. Adding Cu initially produced a rise in digestive enzyme activities with the greatest stimulation occurring at the 13 mg/kg Cu in both pyloric caecum and stomach, followed a decrease in activities. Dietary Cu upregulated Cu-Zn superoxide dismutase (SOD) activity at low concentrations while downregulating it at high concentrations, and malondialdehyde (MDA) level was affected in a contrary manner.