We have studied experimentally for the first time the properties of hydrogen atoms in solid hydrogen under pressure. The recombination rate constant has activation-type temperature dependence in the pressure range from 0 to 22 MPa. The activation energy increases linearly with external pressure E-a = (2.4 P + 106 K), as should be expected in the case of a tunneling vacancy mechanism in atom diffusion. Strong pressure effects on the linewidth of the ESR signal and on the spin-lattice relaxation time T-1 were explained by the competition between the local ortho-para conversion process around the H atom and the pressure-dependent diffusion.