Both mechanical and dielectric relaxation techniques were applied to investigate the microscopic transport mechanism of oxygen ion and to deduce the dynamical relaxation parameters in oxygen ion conductor La2Mo2O9. In the mechanical relaxation measurement, a prominent relaxation peak was observed around 400 K at a measurement frequency of 1 Hz, which is actually composed of two subpeaks (P-1 at lower temperature and P, at higher temperature). As for the dielectric experiment, only one relaxation peak was observed above 600 K when the measurement frequency is greater than 500 Hz. The activation energy and the relaxation time at infinite temperature were determined as (0.9 eV, 3 x 10(-16) s), (1.1 eV, 2 x 10(-16) s), and (0.99 eV, 5 x 10(-14) s) for the P-1 peak, P-2 peak, and dielectric peak, respectively. These relaxation parameters are all in the same range as that for oxygen ion diffusion in oxide ceramics, suggesting a mechanism of short diffusion of oxygen ions for the two kinds of relaxation peaks. Based on the crystalline structure of La2Mo2O9, an atomistic mechanism of oxygen ion diffusion via vacancies is suggested.