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A new neutron detector based on a recoil proton and a microchannel plate (MCP) has been developed for the measurement of ultrafast pulse neutrons. In order to know the performance of the detector, the neutron sensitivity was investigated through simulation and experiment. A model of Monte Carlo simulation was set up for neutron sensitivity simulation. In this model, the yields and average energy of protons emitted from polyethylene targets of different thicknesses were calculated as a function of neutron energy. Then, the yields of secondary electrons produced by the recoil protons in the microchannel of the MCP were also calculated. The neutron sensitivity of the detector was finally obtained. The results show that the detector can achieve a neutron sensitivity of more than 10−15 C cm2 if the neutron energy is greater than 1 MeV. Experiments were performed to test the neutron sensitivity on the accelerator at the China Institute of Atomic Energy. The simulated results agreed with those of the experiments considering the uncertainties. The theoretical model of the detector for the calculation of the neutron sensitivity was correct. The performance of the detector accorded with the anticipative purpose.