Herein, a novel peroxidase-like (POD-like) nanozyme Cu/B-NC was synthesized. The Cu and B co-doped nanozyme Cu/B-NC has competitive POD-like activity but negligible oxidase-like (OXD-like) activity, which is proved to partly benefit from the doping of boron atom. The catalytic activity of Cu/B-NC is high with great affinity for TMB and H2O2 and high reaction velocity. Cu/B-NC was utilized to catalyze the condensation of phenolic substance epinephrine (EP) and 4-aminoantipyrine (4-AAP) to form colored quinone imine in the presence of H2O2. UV–vis absorbance of quinone imine at 492 nm was used for EP determination. Catalase (CAT) could decompose H2O2, so CAT could also be quantified through absorbance variation. The linear ranges of colorimetric detection for EP and CAT were 2–100 μM and 1–30 U mL−1, respectively. The limits of detection (LODs) for EP and CAT were 0.97 μM and 0.57 U mL−1, respectively. The practicability of this sensing platform was further validated by successful application in actual samples.