Copper-based nanozyme has shown the superior in the oxidase-like activities due to its electron transfer ability between the Cu (I) and Cu (II) sites during the catalytic reactions. Herein, a Cu(I)-MOF (Cu-Mel) was readily synthesized by a traditional hydrothermal process using the precursors of Cu+ and melamine, which was then used in the laccase-like catalytic reactions for the first time. Some means, such as X-ray diffraction (XRD), scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS) were employed to character the microstructure of the Cu-Mel. The catalytic oxidation of the 4-aminoantipyrine (4-AP) and 2,4-dichlorophenol (2,4-DP) were adopted to evaluate the laccase-like catalytic ability of the resulting Cu-Mel. The catalytic conditions including the temperatures, the presence of alcohols and the ionic concentrations, were varied to optimize the laccase-like activities, based on that, the highest laccase-like catalytic activity is presented with higher maximum reaction rate (Vmax). The good storage stability is also presented by the Cu-Mel. The Cu-Mel was utilized in the degradation of Congo red, showing a good degradation efficiency. These findings facilitate the development of the laccase mimics and serve as a foundation for the design and applications of Cu-MOFs in the nanozyme realm.