Evolution of vibration relaxation of hydrogen atoms in metals with the close-packed lattice at high and medium temperatures is investigated based on non-equilibrium statistical thermodynamics, in that number on using the retarded two-time Green function method. In accordance with main kinetic equation - the generalized Fokker-Plank- Kolmogorov equation, anharmonism of hydrogen atoms vibration in potential wells does not make any contribution to collision effects. It influences the relaxation processes at the expense of interference of fourth order anharmonism with single-phonon scattering on impurity hydrogen atoms. Therefore, the total relaxation time of vibration energy of system metal-hydrogen is written as a product of two factors: relaxation time of system in harmonic approximation and dimensionless anharmonic attenuation of quantum hydrogen state.