Focusing on the specific self-powered neutron detector (SPND) using rhodium as the emitter material, this paper performs the numerical simulation and sensitivity study for SPNDs used in a typical pressurized water reactor (PWR). The computational model was developed based on a PWR lattice code bamboo lattice and a Monte Carlo code Geant4. In order to validate the model, the neutron sensitivities with single-energy incident neutrons are calculated and compared against the experimental results. Influences of the incident neutron energy spectrum and the emitter burnup to the neutron sensitivity of the SPND are analyzed. Bamboo lattice is used to calculate the incident neutron energy spectrum and the emitter nucleus densities which are the environment of the SPND. Numerical results show that the neutron sensitivity decreases due to the increase of the enrichment, the assembly average burnup, the boron concentration, the moderator temperature, and the burnable poison rods. The increase in the emitter burnup will lead to the decrease of the neutron sensitivity. Taking the incident neutron energy spectrum and the nucleus density into account together, the neutron sensitivity decreases with the increase in the assembly average burnup.