Phase H(MgSiO_4H_2), one of the dense hydrous magnesium silicates(DHMSs), is supposed to be vital to transporting water into the lower mantle. Here the crystal structure, elasticity and Raman vibrational properties of the two possible structures of phase H with Pm and P2/m symmetry under high pressures are evaluated by first-principles simulations. The cell parameters, elastic and Raman vibrational properties of the Pm symmetry become the same as the P2/m symmetry at～ 30 GPa. The symmetrization of hydrogen bonds of the Pm symmetry at ～ 30 GPa results in this structural transformation from Pm to P2/m. Seismic wave velocities of phase H are calculated in a range from 0 GPa to 100 GPa and the results testify the existence and stability of phase H in the lower mantle. The azimuthal anisotropies for phase H are A_(P0)= 14.7%,A_(S0)= 21.2%(P2/m symmetry) and A_(P0)= 16.4%, A_(S0)= 27.1%(Pm symmetry) at 0 GPa, and increase to A_(P30)= 17.9%,A_(S30)= 40.0%(P2/m symmetry) and A_(P30)= 19.2%, A_(S30)= 37.8%(Pm symmetry) at 30 GPa. The maximum V P direction for phase H is [101] and the minimum direction is [110]. The anisotropic results of seismic wave velocities imply that phase H might be a source of seismic anisotropy in the lower mantle. Furthermore, Raman vibrational modes are analyzed to figure out the effect of symmetrization of hydrogen bonds on Raman vibrational pattern and the dependence of Raman spectrum on pressure. Our results may lead to an in-depth understanding of the stability of phase H in the mantle. Phase H (MgSiO_4H_2), one of the dense hydrous magnesium silicates (DHMSs), is supposed to be vital to transporting water into the lower mantle. Here the crystal structure, elasticity and Raman vibrational properties of the two possible structures of phase H with Pm and P2 / m symmetry under high pressures are evaluated by first-principles simulations. The cell parameters, elastic and Raman vibrational properties of the Pm symmetry become the same as the P2 / m symmetry at ~ 30 GPa. The symmetrization of hydrogen bonds of the Pm symmetry at ~ 30 GPa results in this structural transformation from Pm to P2 / m. Seismic wave velocities of phase H are calculated in a range from 0 GPa to 100 GPa and the results testify the existence and stability of phase H in the lower mantle . The azimuthal anisotropies for phase H are A_ (P0) = 14.7%, A_ (S0) = 21.2% (P2 / m symmetry) and A_ (P0) = 16.4%, A_ (S0) = 27.1% 0 GPa, and increase to A P30 = 17.9%, A_ S30 = 40.0% (P2 / m symmetry) and A_ (P30) = 19.2% , A_ (S30) = 37.8% (Pm symmetry) at 30 GPa. The maximum VP direction for phase H is [101] and the minimum direction is [110]. The anisotropic results of seismic wave velocities imply that phase H might be a source of seismic anisotropy in the lower mantle. Furthermore, Raman vibrational modes are analyzed to figure out the effect of symmetrization of hydrogen bonds on Raman vibrational pattern and the dependence of Raman spectrum on pressure. Our results may lead to an in-depth understanding of the stability of phase H in the mantle.