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The self-consistent electronic structure calculations were carried out with the accurate frozen-core full-potential projector augmented-wave method on 13 Ni-Pt intermetallic compounds of simple crystalline structures, i.e. A15, D019, D03 and L12 Ni3Pt and NiPt3, and α-NiAs, B1, B2, L2a, and L10 NiPt. The calculations reveal that the L12 Ni3Pt, L10 NiPt and L12 NiPt3 are energetically more stable than their respective competitive structures, indicating that the three structures may be formed in some appropriate conditions. The obtained results match well with the experimental observation or other theory predictions. It is found that there is hybridization between Ni 3d and Pt 5d states, which may significantly affect the structural stability and magnetism of metastable Ni-Pt intermetallic compounds.