A comprehensive comparison neutronics calculation has been performed to investigate the effect of different reflectors on the tritium production and transmutation of minor actinides in a fusion hybrid reactor. Fusion-Driven Subcritical Spent Fuel Burner hybrid reactor (FDS-SFB), has been chosen as the computational model. All the designs and calculations have been carried out by using SuperMC Monte-Carlo code with ENDF/B-VII neutron cross-section library. Beryllium (Be), beryllium oxide (BeO), HT-9 stainless steel, tungsten carbide (WC), magnesium oxide (MgO), silicon carbide (SiC), and titanium carbide (TiC) have been selected as the candidate reflectors. Other neutronic parameters, such as the neutron flux spectrum as well as the effective multiplication factor (keff), have been calculated for each of the reflectors to understand the behavior of each reflector material. In the case of tritium production, as expected, Be and BeO had the best performance and if a non-beryllium reflector was considered, MgO could be the best. In the case of transmutation of TRUs, for 241Am, 243Am, and 242Pu, BeO had the best results. For 244Cm and 237Np, TiC and MgO were the best choices respectively. For the total transmutation, BeO, MgO, and WC had the best capability to transmute TRUs among the other reflectors. Considering both parameters, i.e., TRUs transmutation and Tritium production, BeO (among beryllium-reflectors) and MgO (among non-beryllium reflectors) could be an appropriate choice to fusion hybrid designs.