Nanozymes have emerged as enzyme-mimicking nanomaterials to overcome the low stability and high cost of some natural enzymes. The design and fabrication of nanozymes with superior performance to natural enzymes are in urgent demand. Single-atom catalysts offer the unique characteristics of maximum atomic utilization, and are an excellent candidate for nanozymes. However, most of the reported synthesis methods for single-atom catalysts require the preparation of supports for single-atom catalysts in advance, which requires multiple steps and calcination in a high temperature atmosphere. Herein, Cu–N–C single-atom nanozymes (Cu–N–C SAzymes) were successfully designed via a one-pot solvothermal method. Cu–N–C SAzymes exhibited excellent peroxidase-mimicking activity that is superior to some other related nanoparticles. The mechanism study revealed that H₂O₂ was catalyzed by Cu–N–C SAzymes to generate reactive oxygen species. Furthermore, based on the excellent peroxidase-mimicking activity of the Cu–N–C SAzymes, a simple and sensitive detection method for H₂O₂ and glucose has been developed.