Abstract: Cs₂LiYCl₆:Ce³⁺(CLYC) crystal is a promising new inorganic scintillator. It can discriminate neutron and γ rays with pulse shape discrimination (PSD) method. Charge comparison method, whose best discrimination result was achieved through optimizing the integral time window width with heavy calculation, was usually adopted to discriminate neutron and γ rays in CLYC. In this work, Fisher linear discriminant, which aims to get high discrimination figure of merit through constructing projective vector, was used to discriminate neutron and γ in CLYC crystal in Am-Be mixed radiation field. The signals from CLYC crystal were digitized using DPO7104 oscilloscope. The results show that after constructing projective vector, Fisher linear discriminant has small calculation and good robustness, and can get better discrimination results than charge comparison method.