The Centrifugal Nuclear Thermal Rocket (CNTR) is a nuclear thermal propulsion (NTP) concept that utilizes extremely high-temperature liquid fuel to directly heat propellant. The liquid fuel is encased within a rapidly rotating cylinder. Compared to conventional solid-fuel NTP designs, the liquid-fuel design enables a significantly higher specific impulse attributed to the elevated temperature of the propellant. In this study, a CNTR core design with 37 centrifugal fuel elements (CFEs) and 12 control drums (CDs) is proposed. This design employs 19.75 wt% enriched uranium as the fuel, with zirconium hydride serving as the moderator. A comprehensive sensitivity study was conducted to optimize key neutronic parameters such as keff, power distribution, and temperature reactivity coefficients, by varying the CFE pitch, reflector thickness, CD design, and poison loading. An addition of 0.225 wt% 167Er to the moderator in the central axial core region, along with the introduction of 0.6 wt% 167Er into the central reflector region, not only can effectively suppress the positive moderator temperature coefficient and the reflector temperature coefficient but also can improve the core axial power distribution. The calculated heat deposition suggests the potential necessity for supplementary cooling for the moderator CDs, and the reflector. A preliminary depletion analysis was conducted to assess the potential impact of xenon and samarium poisoning on core reactivity.