The experiments showed that the addition of copper (Cu) in palladium (Pd) membrane reduces the permeability of hydrogen (H) in Pd, and the permeability of H in body-centered cubic (BCC) PdCu alloy is larger than that in face-centered cubic (FCC) PdCu alloy. The underlying reasons are still not well understood. In the present work, systematical ab initio calculations are carried out to investigate the factors affecting the diffusion properties of H in PdCu alloys. It is found that the lowest diffusion barrier of H with zero-point energy correction in BCC PdCu alloy (0.016 eV) is relatively low than that in FCC PdCu alloy (0.346 eV). The interactions among interstitial H atoms are significantly repulsive in BCC PdCu alloy, while it is attractive in FCC PdCu alloy. The results suggest that it is energetically favorable to form interstitial H cluster in FCC PdCu alloy rather than that in BCC PdCu alloy. The formation of interstitial H clusters impedes the fast movement of H in FCC PdCu alloy. The presence of intrinsic vacancy in FCC PdCu alloy further hinders the migration of H. It is found that the binding strength of vacancy with H in FCC PdCu alloy is much larger than that in BCC PdCu. The stronger the combination of H and vacancy, the greater the obstacle to the movement of H in PdCu alloy. All these results elucidate the experimental phenomena why H penetration ability in FCC PdCu alloy is weaker than that in BCC PdCu alloy.