Copper nanoclusters (CuNCs) have advantages of low cost, excellent biocompatibility, and good fluorescence properties, but they are seldom used as nanozymes for biosensing owing to their low catalytic activity and poor stability. Herein, a natural polymer, chitosan (CS), was explored to effectively promote the peroxidase-like property of glutathione-protected copper nanoclusters (GSH-CuNCs). Due to the synergistic catalytic enhancement and protection effect provided by CS, both peroxidase-like activity and stability of CS@GSH-CuNCs were significantly improved compared with those of GSH-CuNCs. Moreover, upon the addition of H2O2, CS@GSH-CuNCs can catalyze the oxidation of colorless 3, 3′, 5, 5′-tetramethylbenzidine (TMB) to produce oxidized TMB (oxTMB) with blue color, meanwhile, H2O2 can efficiently cause the fluorescence quenching of CS@GSH-CuNCs. Based on that, a dual-signal approach was designed for the detection of H2O2, choline, and acetylcholinesterase (AChE) activity. For the colorimetric assay, this method exhibits detection limit (DL) of 6.7 μM for H2O2, 6.5 μM for choline, and 3.3 mU/mL for AChE activity. For the fluorometric assay, this approach presents DL of 0.6 μM for H2O2, 1.2 μM for choline, and 1.4 mU/mL for AChE activity. Furthermore, this dual-signal assay was applied to milk and human serum, indicating its great prospect for real sample analysis.