The r-process is one of the processes that produce heavy elements in the Universe. One of its possible astrophysical sites is the neutron star - black hole (NS-BH) merger. We first show that the neutrons may be degenerate before and during the r-process in these mergers. Previous studies assumed neutrons were non-degenerate and the related rates were calculated under Maxwell-Boltzmann approximations. Hence, we corrected the related rates with neutron degeneracy and put into the network code and calculated with the trajectories of NS-BH mergers. We show that there are differences in the nuclei distributions and leads to big changes in the heat generation and hence the temperature changes during the r-process. The higher temperatures in the r-process lead to higher luminosity of the light curves of these mergers than the one using non-degenerate rates. However, this has little effect on the final abundances.