Abstract Zirconium (Zr) alloys as cladding materials are widely used in fission reactors. The service life of Zr-based materials cladding is seriously affected by the hydrogen (H) behaviors; while the impurities (C, N and O) in Zr alloys have a great influence on the hydrogen behaviors. In this work, we have investigated the impurity–hydrogen interactions in hexagonal-closed packed Zr (hcp-Zr) by a first-principles approach. It was found that H atom tends to occupy tetrahedral interstitial position in perfect Zr and occupy octahedral interstitial position in Zr with vacancy, while the impurities tend to occupy octahedral interstitial positions in Zr both with and without vacancy. The impurities can trap H atoms. Four possible paths were studied for the diffusion of H atom in hcp-Zr, and it is found that the diffusion barriers of H varied with the presence of impurities.