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 L1(2) structure and two different ones of FIM and A-type AFM for D0(22) 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 L1(2) FIM is most stable among all of the aforementioned states. For D0(22), AFM is more stable than FIM by a significant energy difference (102 meV/Cr-atom). For D0(22) 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 mu(B) for FIM, A-, C-, and G-type AFM in L1(2), and 2.36, 2.59 mu(B) for FIM and AFM in D0(22), respectively. The magnetism is proven to be very sensitive to a crystal structure. (C) 2003 American Institute of Physics.