This communication reports the measurement of direct response for fast and thermal neutrons of a newly marketed scintillation crystal LaBr2.85Cl0.15:Ce, along with the widely used LaBr3:Ce and NaI:Tl crystals. It continues our investigation on the possible utility of LaBr2.85Cl0.15:Ce crystal for the detection of high-energy γ-rays and neutrons. This is the first report of the neutron response of the LaBr2.85Cl0.15:Ce crystal. The neutron response was measured for the three detectors using a calibrated Am-Be source, which emits both neutrons and γ-rays. To eliminate the events due to the interaction of the 4.4 MeV γ-ray emitted from Am-Be, the γ-ray response of all three crystals was simulated using the Monte Carlo simulation toolkit GEANT4. Events due to 2.22 MeV γ-ray produced by the capture of thermal neutrons in the paraffin moderator were also eliminated with the aid of simulations. In addition, the response due to fast neutrons was also simulated using GEANT4 and compared with the measured spectrum. This is the first report of the simulation of fast neutron response of LaBr2.85Cl0.15:Ce using GEANT4. The fast neutron detection efficiency of the three detectors has been obtained from the measured spectra.