An 8-week feeding trial was conducted to determine the dietary copper (Cu) requirement and its effect on the non-specific immune responses of juvenile grass shrimp, Penaeus monodon. Purified diets with seven levels (0, 10, 20, 30, 40, 80, 160mg Cu kg diet−1) of supplemental Cu were fed to P. monodon (mean initial weight 0·29±0·004g). Each diet was fed to three replicate groups of shrimp. The rearing water contained 1·53μg Cu l−1. Shrimp fed diets supplemented with 10 and 20mgCukg diet−1 had significantly (P< 0·01) greater weight gain, feed efficiency (FE) and protein efficiency ratio (PER) than those fed the unsupplemented control diet and diets supplemented with ≧40mgCukg diet−1. Whole body Cu concentration in shrimp generally increased as dietary Cu supplementation increased. Total haemocyte count (THC) was higher in shrimp fed diets supplemented with 10–30mgCukg diet−1 than shrimp fed the unsupplemented control diet and diets supplemented with ≧40mgCukg diet−1. Intracellular superoxide anion (O−2) production ratios were significantly higher in shrimp fed diets supplemented with 10–30mgCukg diet−1 than shrimp fed the diet supplemented with 160mgCukg diet−1. Analysis by polynomial regression of weight gain percent, FE and by linear regression of the whole-body Cu retention of shrimp indicated that the adequate dietary Cu concentration in growing P. monodon is about 15–21mgCukg diet−1. The immune indicators suggest that an adequate dietary Cu concentration for non-specific immune responses in P. monodon is about 10–30mgCukg diet−1.