A scintillator detector consisting of LaBr3(Ce) (0.5%) scintillator and PMT, and an oscilloscope were used to study the neutron sensitivities of LaBr3(Ce) scintillator at the CSNS Back-n white neutron source in the double-bunch and single-bunch operation modes, respectively. Under the two operation modes, the relative neutron sensitivity curves of the LaBr3(Ce) scintillator in the energy region between 1 and 20 MeV, and 0.5 and 20 MeV were obtained for the first time. In the energy range of 1-20 MeV, the two curves were nearly identical. But the relative neutron sensitivity uncertainties of the double-bunch experiment were higher than those of the single-bunch experiment. The above results indicated that the single-bunch experiment's neutron sensitivity curve has a lower minimum measurable energy than the double-bunch experiment. Above the minimum measurable energy of the double-bunch experiment, there is little difference between the measured relative neutron sensitivity curves of the single-bunch and double-bunch experiments of the LaBr3(Ce) scintillator and those of other scintillators with a similar neutron response signal intensity.