Heavy metal contamination has a severe impact on ecological health and plant growth and is becoming increasingly serious globally. Copper (Cu) is a heavy metal that is essential for the growth and development of plants, including peach (Prunus persica L. Batsch); however, an excess is toxic. In plants, amino acids are involved in responses to abiotic and biotic stresses, such as water deficit, extreme temperatures, high salinity, and heavy metal stress. However, the role of leucine in the regulation of heavy metal stress is currently unclear. Therefore, we investigated the effects of exogenous leucine on the growth of peach seedlings under Cu stress. Exogenous leucine improved the leaf ultrastructure and ionic balance and increased the chlorophyll content, the net photosynthetic rate, and the maximum photochemical efficiency. Furthermore, it attenuated Cu-stress-induced oxidative damage via a decrease in reactive oxygen species (ROS) and the regulation of the antioxidant and osmotic systems. These effects, in turn, ameliorated the reductions in cell viability, cellular activity, and biomass under Cu stress. Moreover, exogenous leucine increased the activities of nitrate reductase (NR), glutamine synthetase (GS), and glutamic acid synthetase (GOGAT) and thus improved the nitrogen metabolism efficiency of plants. In conclusion, leucine significantly improved the photosynthetic performance and antioxidant capacity, reduced Cu accumulation, and promoted nitrogen metabolism, which in turn improved the resistance of peach seedlings to Cu stress.