Potential energy curves (PECs) for the ground state and the second excited state (a3Π and A1Π) of SnO molecule are calculated by using the multi-reference configuration interaction method (MRCI) and also considering Davidson correction’ multi-reference configuration interaction method with aug-cc-pvTZ basis for O atom, aug-cc-pvTZ-PP basis for Sn atom, respectively. On the basis of the PECs, the Re, ωe, ωeχe, Be, Te and De are obtained. The symmetries and dissociation limits for these electronic states are determined by group theory. The results show that three electronic states are dissociated along the same channel, Sn (3P)+O (3P). And then the PECs are fitted by using level program. The spectroscopic constants are determined according to fitted results, which shows that MRCI results are in good agreement with the experimental values. By solving the radial Schrödinger equation of nuclear motion, the vibration levels can be obtained, molecular constant (Bv and Dv) are reported for the first time at J=0.