The effect of hydrogen on the physical-chemical properties of copper is directly dependent on the types of chemical bonding between H and lattice defects in Cu. In this work, we performed a systematic study of the bonding of H-atoms with crystal lattice defects of copper. This included three types of symmetric tilt grain boundaries (GBs), sigma 3, sigma 5 and sigma 11, and the low Miller index surfaces, (111), (110) and (100). A comparison with literature data for the bonding of H-atoms with point defects such as vacancies was done. From the defects investigated and analyzed, we conclude that the bond strength with H-atoms varies in the decreasing order: surfaces [(111), (110) and (100)] > vacancy > sigma 5 GB > sigma 11 GB > bulk approximate to sigma 3 GB. A study on the effects of the fcc lattice expansion on the binding energies of H-atoms shows that the main driving force behind the segregation of H-atoms at some GBs is the larger volume at those interstitial GB sites when compared to the interstitial bulk sites.