Highly oriented ZnO nanorod (NR) arrays were fabricated on a seeded substrate through a hydrothermal route. The prepared ZnO nanorods were used as an amperometric enzyme electrode, in which glucose oxidase (GOx) was immobilised through physical adsorption. The modified electrode was designated as Nafion/GOx/ZnO NRs/ITO. The morphology and structural properties of the fabricated ZnO nanorods were analysed using field-emission scanning electron microscope and X-ray diffractometer. The electrochemical properties of the fabricated biosensor were studied by cyclic voltammetry and amperometry. Electrolyte pH, electrolyte temperature and enzyme concentration used for immobilisation were the examined parameters influencing enzyme activity and biosensor performance. The immobilised enzyme electrode showed good GOx retention activity. The amount of electroactive GOx was 7.82 × 10−8 mol/cm2, which was relatively higher than previously reported values. The Nafion/GOx/ZnO NRs/ITO electrode also displayed a linear response to glucose ranging from 0.05 mM to 1 mM, with a sensitivity of 48.75 µA/mM and a low Michaelis–Menten constant of 0.34 mM. Thus, the modified electrode can be used as a highly sensitive third-generation glucose biosensor with high resistance against interfering species, such as ascorbic acid, uric acid and L-cysteine. The applicability of the modified electrode was tested using human blood samples. Results were comparable with those obtained using a standard glucometer, indicating the excellent performance of the modified electrode.