We report on the growth of NdFeAs(O,H) epitaxial thin films on MgO (001) substrates and their electrical transport properties. The maximum carrier density of the NdFeAs(O,H) films was more than twice as large as that of our NdFeAs(O,F) films. This enabled us to investigate the physical properties of heavily electron doped NdFeAsO, which could not be achieved with NdFeAs(O,F). The irreversibility field H irr of NdFeAs(O,H) was larger than that of NdFeAs(O,F) for H || c due to the decrease in the anisotropy of the upper critical field. A very high critical current density of 17 MA cm −2 was recorded at 4 K, which corresponds to about 13% of the depairing current density of NdFeAs(O,F).