Abstract: CASTEP module based on the density functional theory（DFT） is used to optimize the structure of fluorapatite unite cell and obtained the band structure，density of states， and Mulliken population. Then 3 different fluorapatite （001）cleavage surfaces，the Ca1，Ca1-Ca1，PO4 termination，were established and optimized，and their surface energy were calculated respectively. The results show that fluorapatite is an insulator with a band gap of 5.657 eV，and its band is mainly distributed between -38.5 eV to -15.1 eV. O3-Ca1 bond has the smallest population value and is most easily broken of all bonds in the fluorapatite bulk. O3 contributes most near Fermi level，easy to participate in physical and chemical reactions as active site. The results also show that the Ca1 terminal surface have the lowest surface energy，become the most stable surface. Moreover，electron density difference plot of the optimum（001）surface shows that compared with O3-Ca1， O3-Ca2 shares more electrons，has stronger interactions，and are more difficult to break，which is consistent with the Mulliken population analysis result. The first-principles calculation results provide reference and guidance for the construction of a perfect genetic mineral processing database and the selection of a fluorapatite flotation process.

Key words: Fluorapatite, First-principles, CASTEP, Crystal genes, （001 ）cleavage surface