To resolve the discrepancy between the numerical detonation cell size and experimental observations, simulations are conducted with a detailed thermochemical reaction model for a premixed argon-diluted hydrogen-oxygen mixture. Four different scenarios are considered: (i) The whole system is in thermodynamic equilibrium; (ii) the vibrational relaxation is considered and the translational-rotational temperature is used as the dominant temperature of the chemical reactions; (iii) the same non-equilibrium effect as in the second scenario is used along with Park's two-temperature model to account for the effect of vibrational temperature on chemical reaction rates; and (iv) a more physically consistent vibration-chemistry-vibration coupling model is adopted. The simulated detonation cell widths for the first and second scenarios are significantly lower than the experimental measurements, whereas reasonable agreement is observed for the third and fourth scenarios. These results confirm that the involvement of vibrational relaxation in the chemical reactions is an important mechanism in gaseous detonation.