This thesis presents a preliminary neutron shielding design for the HTS coils of a centrifugally confined fusion space propulsion system, which is a promising technology for future space travel. The design process involved a comprehensive study of neutron transport, material selection, and shielding optimization using MCNP and MATLAB simulations. First, the neutron attenuating properties of reflector, moderator, and absorber candidate materials were compared in MCNP. The thickness and composition of the shield were optimized from the resulting MCNP data. Next, two overall reactor and shielding geometry models were developed in MATLAB to estimate the total mass of the HTS shielding for both coils. The first model assumed a point neutron source and uniform thickness across the surface area of the shield. The second model improved upon the first by considering a source distribution and the varying distance between the source and surface of the shield. Both D-T and D-D fuel cases were run with the model and the resulting mass estimates were used to compare the specific mass to the state-of-the-art technology.