Abstract: Hydrous magnesium silicate is considered as a potential water-rich reservoir in the early Earth's interior. Investigating its behavior under extreme high-temperature and high-pressure conditions is crucial for understanding the internal structure models and water presence potential of super-Earths. By using first-principles molecular dynamics simulations, this study systematically investigates the stability and elastic properties of β-Mg₂SiO₅H₂ within the pressure range of 500-900 GPa and temperature range of 2000-6000 K. The results indicate that the system remains thermodynamically stable across the entire studied pressure-temperature range, with no structural phase transitions observed. Calculations of the mean square displacement reveal the transition interval for the superionic state: at 500 GPa and 2000 K, 700 GPa and 3000 K, and 900 GPa and 3100 K, all atoms remain confined within the lattice, with the system in a normal state. When the temperature increases to 500 GPa and 4000 K, 700 GPa and 5000 K, and 900 GPa and 6000 K, the mean square displacement of H atoms exhibits a linear increase, while the framework atoms (Mg, Si, O) remain localized. The proton trajectories form a diffuse network, exhibiting the characteristics of a superionic state with a "solid framework + liquid-like ions". Simulation results show that the density of β-Mg₂SiO₅H₂ increases linearly with pressure. The shear modulus decreases nearly linearly with increasing temperature, while the bulk modulus shows a significant reduction at 900 GPa and 6000 K, likely in response to the transition to the superionic state. The variations in shear wave velocity and compressional wave velocity are primarily controlled by pressure and temperature, increasing with pressure and decreasing with temperature. Under high pressure (900 GPa), the superionic state leads to a notable decrease in the compressional wave velocity of β-Mg₂SiO₅H₂, suggesting that the superionic transition induces structural softening. This study confirms that β-Mg₂SiO₅H₂ can remain stable under the deep mantle pressure-temperature conditions of super-Earths with masses 5-8 times that of Earth and can transition to a superionic state under specific conditions. Its high water content of up to 11.4 wt% and efficient proton transport capability have significant implications for deep water cycles and the habitability of terrestrial planets, providing key theoretical insights for understanding planetary interior dynamics.