In this study, we have employed the first-principles density functional theory (DFT) computational method to predict the influence of surface segregation on the magnetic properties of small L10 CoPt nanoparticles. For both the modelled cuboidal (with a chemical formula of Co26Pt12) and cuboctahedral (with a chemical formula of Co18Pt20) CoPt nanoparticles, the DFT calculations predict that Pt surface segregation should occur thermodynamically. Associated with this Pt surface segregation, the surface-segregated CoPt magnetic nanoparticles are predicted to have significantly reduced magnetic moments and magnetic anisotropy energies than those of the corresponding bulk-terminated (i.e. non-segregated) nanoparticles. Hence, our study suggests that surface segregation could deteriorate the magnetic properties of CoPt nanoparticles.