Laser-driven neutron source is possible to obtain data with higher energy resolution than accelerator based neutron source. The purpose of this study is to evaluate the neutron pulse width for the energy spectrum emitted by the reaction between charged particles experimentally obtained by LFEX laser and a beryllium neutron production target. Monte Carlo simulation code of PHITS 3.02 was used for neutron pulse width evaluation.Furthermore, we investigate the candidate of scintillator for the detection of neutrons in laser-driven neutron source. It was confirmed that the neutron pulse width of a laser-driven neutron source was shorter than that of the accelerator based neutron source in the keV to MeV region. We also experimentally confirmed that organic scintillator such as p-terphenyl was the candidate for the detection of keV to MeV energy region neutron because of high light output and fast decay.