We used the first-principles density functional theory (DFT) to predict the magnetic properties of (1 0 0), (0 0 1), (1 0 1), (1 1 0), and (1 1 1) surfaces of L10 ordered CoPt alloy. Our results indicate that bulk-terminated CoPt surfaces exhibit magnetic moment higher than that of bulk CoPt crystal and surface magnetic anisotropy favoring in-plane magnetization. Moreover, our DFT calculations predict that Pt prefers to segregate to the outermost layer of all these five CoPt surfaces with energy gain in the range of 0.05-0.47 eV for each segregated Pt atom. Comparing the structural and magnetic properties of the bulk-terminated and Pt-segregated CoPt surfaces, we found that Pt surface segregation led to larger contraction relaxation, reduced magnetic moments (with the exception of (1 1 0) surface), smaller spin canting angles, and an out-of-plane contribution to the surface magnetic anisotropy energy of the CoPt surfaces. Furthermore, our electronic structure analysis suggests that the change in the density of [Formula: see text] minority spin states of surface Co atoms mainly underlies the observed phenomena related to the surface magnetism of L10 CoPt alloy.