A kinetic model of fermentative hydrogen (H2) production was developed for the hyperthermophilic marine bacterium Thermotoga neapolitana DSMZ 4359T using glucose as the substrate. The model was built based on anaerobic digestion model no.1 (ADM1) by IWA using Monod-like kinetic equations. Several series of pH controlled batch fermentation tests were performed under pure CO2 or N2 atmosphere in serum bottles to evaluate the growth kinetic parameters. The kinetic parameters were estimated by applying the non-linear least square method to Monod and Michaelis–Menten kinetic equations. The experimentally estimated value of k, kS, Y and kd were 0.839 h−1, 1.42 g/L, 0.1204 and 0.0043 h−1, respectively. The kinetic parameters were analyzed for sensitivities and subsequently calibrated and validated by a separate set of experimental results. The model was particularly effective in estimating the biomass growth, substrate consumption, and H2 production except for acetate and lactate production, due to capnophilic condition (under CO2 atmosphere).