Theoretical prediction on the elastic properties of superionic material is challenging due to the fast diffusion of cation/anion in the lattice. Here, we investigated the elastic properties of Li₂O at elevated temperature and pressure using ab initio molecular dynamics (AIMD). We observed the superionic transition above 1300 K, and the highly diffusive Li(+ )leads to local structure change with significant influence on the elasticity of Li₂O. We successfully predicted the significant C-11 softening above 1300 K, and the calculated elastic constants fit the previous experimental results very well. It suggests the anharmonic lattice vibration before superionic transition and the diffusion of Li+ after superionic transition are very important for the prediction on the elastic properties, and the AIMD method is able to describe the superionic behavior accurately. In addition, we calculated the bulk and shear moduli, sound velocities, as well as elastic and sound velocity anisotropies. We found that the superionic state transition also leads to the weakening of the elastic and sound velocity anisotropies in Li₂O. Pressure has negative effect on the mobility of Li₂O which strengthens the elastic stiffening effect of superionic Li₂O with increasing pressure.