Copper is a mineral element, which is necessary for the normal growth and development of plants, but high levels of copper will seriously damage plants. Studies have shown that AtGR1 improves the tolerance of Arabidopsis to aluminum and cadmium stress. However, the role of GR in the copper stress response of plants is still unclear. Here, we identified four genes (named BcGR1.1, BcGR1.2, BcGR2.1 and BcGR2.2, respectively) encoding glutathione reductase (GR) in non-heading Chinese cabbage (Brassica campestris (syn. Brassica rapa) ssp. chinensis), which could be divided into two types based on the subcellular localization. Among them, BcGR1.1, which belonged to the cytoplasmic localization type, was significantly upregulated under copper stress. Compared to WT (the wild type), Arabidopsis thaliana heterologously overexpressed BcGR1.1 had longer roots, higher fresh weight, higher GSH levels and GSH/GSSG (oxidized form of GSH) ratio, and accumulated more superoxide dismutase and peroxidase under copper stress. However, in the AsA-GSH cycle under copper stress, the contents of AsA and AsA/DHA were significantly downregulated, and the contents of DHA and T-AsA (total AsA) were upregulated, in the BcGR1.1-overexpressing Arabidopsis. Therefore, BcGR1.1 could improve the scavenging ability of reactive oxygen species (ROS) by increasing the activity of GR, antioxidant enzymes and the utilization of AsA, and then enhance the copper stress tolerance of plants.