The novel oxide-ion conductors (La1-xAx)2Mo2O9-δ (A = Ca, Bi, K, x = 0 ~ 0.075) are investigated in this paper by internal friction and dielectric relaxation techniques. Two relaxation peaks associated with the short-distance diffusion of oxygen vacancies were observed, indicating that there are at least two relaxation processes for diffusion of oxygen vacancies. Doping at La site with different elements shifts both relaxation peaks toward higher temperature and increases the activation energy of oxygen vacancy diffusion. In the case of internal friction, the height of the higher-temperature peak (dominant component) decreases with increasing doping content. In the case of dielectric relaxation, however, the variation of the peak heights as a function of doping content exhibits a maximum around 2.5 % K and 5 % Bi. After properly doping, the conductivity at low temperature of doped La2Mo2O9 increases by different degrees, and a peak of the conductivity at 500° C is observed in the doping content where the highest dielectric relaxation peak appears. Based on the experimental results and the crystalline structure, the mechanism of oxygen vacancy diffusion in (La1-xAx)2Mo2O9-δ samples is discussed.