It is shown that the problem of infrared divergences in the quantum theory of a gravitational field in a vacuum, which are caused by its selfaction, can be solved by the same method as in electrodynamics. Omitting the questions of ultraviolet divergences, the Hamiltonian of the asymptotic dynamics of the gravitational field is computed. The relativistically invariant space of asymptotic states is constructed, on which a modified S-matrix without infrared divergences is defined.