Neutron detection techniques play an important role in various fields. As one of the promising candidates of neutron detectors with high efficiency, rare-earth-ion-doped LiCaAlF6 (LiCAF) scintillators have been developed. Since the LiCAF scintillator consists of light elements, it has low gamma-ray sensitivity. A large single crystal of a LiCAF up to a few inches diameter can be fabricated with Czochralski technique. The large LiCAF scintillator can be a promising neutron detector with high detection efficiency both from thermal to epi-thermal energy region. When using a large crystal, we must take care of the influence of gamma rays because neutron fields are usually accompanied by a large amount of gamma rays. A Ce:LiCAF scintillator can discriminate neutron and gamma-ray events with a pulse shape discrimination based on a difference in scintillation decay time. In this paper, we adopt the digital signal processing technique to investigate the detail properties of the scintillation decay time and evaluate the performance of neutron-gamma discrimination. A Ce:LiCAF scintillator has quite fast component about 1 ns only for fast electrons produced by gamma-rays. There is no fast component for heavy charged particles produced by neutron captures. We, therefore, can discriminate the neutron and gamma-ray events by presence of this fast component. The responses of Ce:LiCAF scintillators were investigated through basic experiments using both a Cf-252 neutron source with a polyethylene moderator and a Co-60 gamma-ray source. By using the pulse shape discrimination based on the presence of fast component, the gamma-ray sensitivity can be reduced to 1/10 of that without the pulse shape discrimination under condition keeping the 90% neutron sensitivity. In addition, we preliminarily evaluate the gamma-ray rejection performance for various Ce content LiCAF crystals. In these evaluations, low Ce content samples showed high gamma-ray rejection property.