An enzymatic biofuel cell (BioFC) is scientifically important because the biofuel can be the glucose solution in a human body and the catalyst uses some kind of organic enzymes instead of the traditional noble metal. Electricity is produced from the bio-electrochemical reaction in which the glucose is oxidized at the anode and oxygen molecules are reduced at the cathode. Products are only the gluconic acid and a water molecule in the overall reaction. Two major factors that influence the cell performance are identified. The first one is the proton (positive ion) diffusion rate in the electrolytic solution. The second one is the oxygen reduction rate at the cathode. This thesis investigates both the proton transport phenomenon near the anode and the catalytic mechanism of oxygen reduction at the cathode. In order to investigate the diffusion process of the protons in a nano-scale environment, molecular dynamics (MD) simulation techniques were employed. All the complex biological molecules involved in the transport were structured using a semi-empirical quantum mechanics (QM) method. Hydronium ions (a proton bond to a water molecule) are the major observation target to trace the trajectory. The diffusion coefficient and the ionic conductivity can be evaluated from the MD simulation results. The first conclusion can be drawn here that the greater the glucose concentration, the better the hydronium diffusivity. In the nano-scale environment, the enzyme promotes the production of protons, but it also plays an obstacle in the hydronium diffusion path. In order to improve the low diffusion mechanism and to increase the cell performance, an external magnetic field is applied to the simulation. The simulation model comprised an Au electrode, PQQ (pyrrolo quinoline quinine), FAD (flavin adenine dinucleotide), and glucose molecules with prescribed hydronium ions in the aqueous solution. A constant magnetic field is applied perpendicularly to the major direction of the diffusion path. It is found that the magnetic field strength is able to enhance the hydronium diffusivity in the solution and the rate of the biochemical reaction is increased. An example of simulation results reveals that the hydronium diffusivity can be increased from m2/s to a maximum m2/s at the glucose concentration 27 mM. The external magnetic field is an easy and feasible technique to improve the BioFC performance significantly. In the last part, a density functional theory (DFT) was introduced to investigate a simplified catalytic mechanism of the oxygen reduction at the cathode. The adsorption process of an oxygen molecule on the metal surface (of the enzymatic reaction center) is analyzed. The rate-limited first proton transfer is also evaluated. The catalytic process plays the key role for further improvement of the BioFC performance.