The properties of hydrogen atoms in a nano-diamond grain surrounded by an amorphous carbon shell are studied with Tight Binding computer simulations. Our samples model nano-diamond grains, of a few nanometers in size, that nucleate within an amorphous carbon matrix, as observed in deposition from a hydrocarbon rich plasma. The calculations show that the average hydrogen interstitial formation energy in the amorphous region is lower than in the nano-diamond core, therefore hydrogen interstitial sites in the in the amorphous region are more stable than in the nano-diamond core. This formation energy difference is the driving force for the diffusion of hydrogen atoms from nano-diamond grains into amorphous carbon regions. An energy well was observed on the amorphous side of the nano-diamond amorphous carbon interface: hydrogen atoms are expected to be trapped here. This scenario agrees with experimental results which show that hydrogen retention of diamond films increases with decreasing grain size, and suggest that hydrogen is bonded and trapped in nano-diamond grain boundaries and on internal grain surfaces.