The purpose of this work is developing of the statistical model of hydrogen diffusion in the crystal lattice of BCC metals with an estimate of the contribution of quantum effects and deviations from the Arrhenius equation. The values of the statistical model calculations of H diffusion coefficients in Fe, V, Nb and Ta are in good agreement with the experimental data. The statistical model can also explain deviations from the Arrhenius equation at temperatures 300-500 K in Fe and Nb. The downward deviation of the diffusion coefficient at 300K can be explained by the fact that the statistical model does not consider the tunneling effect at temperatures below 300K. It was suggested that thermally activated fast tunnelling transition of hydrogen atoms through the potential barrier at temperatures below 500 K provides an almost free movement of H atoms in the α-Fe and V. Using the statistical model allows for the prediction of the diffusion coefficient for H in BCC metals at intermediate temperatures.