Neutronics and thermal-hydraulics design and analyses of the pellet bed reactor for nuclear thermal propulsion are performed based on consideration of reactor criticality, passive decay heat removal, maximum fuel temperature, and subcriticality during a water flooding accident. Besides calculating the dimensions of the reactor core to satisfy the excess reactivity requirement at the beginning-of-mission of 1.25 $ (keff of 1.01), the TWODANT discrete ordinates code is used to estimate the radial and axial fission power density profiles in the core. These power profiles are used in the nuclear propulsion thermal-hydraulic analysis model (NUTHAM-S) to determine the two-dimensional steady-state temperature, pressure, and flow fields in the core and optimize the orificing in the hot frit to avoid hot spots in the core at full-power operation.