The moisture barrier properties of stacked graphene layers on Cu surfaces were investigated with the goal of improving the moisture barrier efficiency of single-layer graphene (SLG) for Cu metallization. SLG with large grain size were stacked on Cu surfaces coated with CVD-SLG to cover the grain-boundaries and defective areas of the underneath SLG film, which was confirmed to be oxidized by Raman spectroscopy measurements. To evaluate the humidity resistance of the graphene-coated Cu surfaces, temperature humidity storage (THS) testing was conducted under accelerated oxidation conditions (85 °C and 85% relative humidity) for 100 h. The color changes of the Cu surfaces during THS testing were observed by optical microscopy, while the oxidized Cu into Cu2O and CuO was detected by X-ray photoelectron spectroscopy (XPS). The experimental results were accord with the results of first-principle simulation for the energetic barrier against water diffusion through the stacked graphene layers with different overlap. The results demonstrate the efficiency of SLG stacking approach against moisture for Cu metallization.