Developing carbon-based materials with high catalytic performance and sensitivity has significance in low-cost and highly efficient nanozymes. Herein, for the first time, Cu,N-codoped hollow carbon nanospheres (CuNHCNs) with highly active Cu-Nx sites were successfully assembled through a template-free strategy, in which Cu2+-poly(m-phenylenediamine) (Cu-PmPD) nanospheres were utilized as the source of Cu, N and C. Benefiting from the synergistic effect of the hollow spherical structure and optimized composition, the CuNHCN exhibits high affinity for 3,3',5,5'-tetramethylbenzidine and H2O2 with 0.0655 mM and 0.918 mM, respectively, which are superior to those of HRP and most metal-based nanozymes. Moreover, by employing glucose and ascorbic acid (AA) as biomolecule models, a CuNHCN-based colorimetric detection platform is developed. The CuNHCN exhibits superior peroxidase mimicking activity and sensitivity in detecting glucose and AA with a detection limit of 0.187 μM and 68.9 nM (S/N = 3), respectively. Also, the colorimetric detection based on the CuNHCN towards glucose and AA in human serum presents superior practicability and accuracy. The assay provides a new avenue for designing and fabricating low-cost peroxidase nanozymes with high performance in bioassays.