In this study, an electrospun regenerated cellulose (RC) nanofibrous membrane with fiber diameters of ∼200-400 nm was prepared first; subsequently, 2-hydroxyethyl methacrylate (HEMA), 2-dimethylaminoethyl methacrylate (DMAEMA), and acrylic acid (AA) were selected as the monomers for surface grafting of polymer chains/brushes via the atom transfer radical polymerization (ATRP) method. Thereafter, four nanofibrous membranes (i.e., RC, RC-poly(HEMA), RC-poly(DMAEMA), and RC-poly(AA)) were explored as innovative supports for immobilization of an enzyme of bovine liver catalase (CAT). The amount/capacity, activity, stability, and reusability of immobilized catalase were evaluated, and the kinetic parameters (Vmax and Km) for immobilized and free catalase were determined. The results indicated that the respective amounts/capacities of immobilized catalase on RC-poly(HEMA) and RC-poly(DMAEMA) nanofibrous membranes reached 78 ± 3.5 and 67 ± 2.7 mg g(-1), which were considerably higher than the previously reported values. Meanwhile, compared to that of free CAT (i.e., 18 days), the half-life periods of RC-CAT, RC-poly(HEMA)-CAT, RC-poly(DMAEMA)-CAT, and RC-poly(AA)-CAT were 49, 58, 56, and 60 days, respectively, indicating that the storage stability of immobilized catalase was also significantly improved. Furthermore, the immobilized catalase exhibited substantially higher resistance to temperature variation (tested from 5 to 70 °C) and lower degree of sensitivity to pH value (tested from 4.0 and 10.0) than the free catalase. In particular, according to the kinetic parameters of Vmax and Km, the nanofibrous membranes of RC-poly(HEMA) (i.e., 5102 μmol mg(-1) min(-1) and 44.89 mM) and RC-poly(DMAEMA) (i.e., 4651 μmol mg(-1) min(-1) and 46.98 mM) had the most satisfactory biocompatibility with immobilized catalase. It was therefore concluded that the electrospun RC nanofibrous membranes surface-grafted with 3-dimensional nanolayers of polymer chains/brushes would be suitable/ideal as efficient supports for high-density and reusable enzyme immobilization.