The negatively charged (at pH 8.2) glucose oxidase (GOx, pI ca. 4.2) was assembled onto the surface of single-walled carbon nanotubes (SWNT), which was covered (or wrapped) by a layer of positively charged polyelectrolyte poly(dimethyldiallylammonium chloride) (PDDA), via the electrostatic interaction forming GOx-PDDASWNT nanocomposites. Fourier transform infrared (FTIR), UV-Vis and electrochemical impedance spectroscopy (EIS) were used to characterize the growth processes of the nanocomposites. The results indicated that GOx retained its native secondary conformational structure after it was immobilized on the surface of PDDA-SWNT. A biosensor (Nafion-GOx-PDDA-SWNT/GC) was developed by immobilization of GOx-PDDA-SWNT nanocomposites on the surface of glassy carbon (GC) electrode using Nafion (5%) as a binder. The biosensor showed the electrocatalytic activity toward the oxidation of glucose under the presence of ferrocene monocarboxylic acid (FcM) as an electroactive mediator with a good stability, reproducibility and higher biological affinity. Under an optimal condition, the biosensor could be used to detection of glucose, presenting a typical characteristic of Michaelis-Menten kinetics with the apparent Michaelis-Menten constant of KM^app ca. 4.5 mmol/L, with a linear range of the concentration of glucose from 0.5 to 5.5 mmol/L (with correlation coefficient of 0.999) and the detection limit of ca. 83 μmol/L (at a signal-to-noise ratio of 3). Thus the biosensor was useful in sensing the glucose concentration in serum since the normal glucose concentration in blood serum was around 4.6 mmol/L. The facile procedure of immobilizing GOx used in present work would promote the developments of electrochemical research for enzymes (proteins), biosensors, biofuel cells and other bioelectrochemical devices.