In order to investigate systematically the magnetic structures of CrPt3, four different magnetic structures of ferrimagnetism (FIM), A-, C-, and G-type antiferromagnetism (AFM) for L12 structure and two different ones of FIM and A-type AFM for D022 structure were calculated. The full-potential linearized augmented plane wave (FLAPW) method was employed to solve Kohn–Sham equation self-consistently, using general gradient approximation for exchange-correlation potential. We found that L12 FIM is most stable among all of the aforementioned states. For D022, AFM is more stable than FIM by a significant energy difference (102 meV/Cr–atom). For D022 AFM the coupling between Cr and Pt atoms is ferromagnetic unlike FIM. The calculated magnetic moments are calculated to 2.78, 2.81, 2.81, and 2.88 μB for FIM, A-, C-, and G-type AFM in L12, and 2.36, 2.59 μB for FIM and AFM in D022, respectively. The magnetism is proven to be very sensitive to a crystal structure.