We have analyzed the diffusion behavior of interstitial hydrogen in bcc iron and niobium using path-integral centroid molecular dynamics (CMD) method, which can describe the real-time evolution of particles based on quantum statistical mechanics. In this study, the embedded-atom-method (EAM) potential model for the iron-hydrogen interaction is developed to reproduce the ab initio minimum energy path of hydrogen migration based on the density functional theory (DFT) data in the literature, while the description of niobium-hydrogen interaction is based on an empirical potential model. Time evolutions of mean-square displacements of hydrogen atoms in the two bulk metals are calculated at various temperatures, and then diffusion coefficients and activation energies of hydrogen migration are evaluated. Especially in the case of iron, the results are in good agreement with experimental measurements over a wide temperature range. In order to characterize the quantum effects on the hydrogen diffusion process, the CMD results are compared with those obtained from classical molecular dynamics method. The obtained results indicate that the quantum effects can play a significant role in hydrogen diffusivity over a wide temperature range in these bcc metals.