A common industrial byproduct known as hydrogen peroxide, which is an essential intermediate, is associated with oxidative damage to brain cells and a number of neurodegenerative disorders. Although catalases are enzymes capable of decomposing hydrogen peroxide into water and oxygen, the low stability of free enzymes limits their industrial use. In the current study, poly(ε‐caprolactone)/polyethyleneimine nanofibers were fabricated using the electrospinning process and catalase was subsequently immobilized via coordination of Cu2+ ions. The characterization of the catalase‐immobilized nanofibers and their catalytic activity for hydrogen peroxide decomposition was evaluated by comparing the free catalase. The studies conducted in the pH range of 5.0–8.5 revealed that the catalase‐immobilized nanofibers had their highest levels of enzyme activity at pH 7.0. When compared to free catalase, it was shown that the thermal stability and storage stability of catalase‐immobilized nanofibers were significantly improved. Catalase‐immobilized nanofibers showed significant reusability, where activity was maintained by around 60% after five repeating cycles. The findings showed that catalase‐immobilized PCL/PEI‐Cu2+ nanofibers had a high potential for various industrial applications as a substitute for the existing techniques.