The potential energy curves (PECs) of X1Σ+ and A1Π electronic states of the SiSe molecule are calculated using the internally contracted multireference configuration interaction approach with the Davidson modification (MRCI+Q) with the correlation-consistent basis sets, aug-cc-pV5Z and aug-cc-pVQZ. In order to improve the quality of the PEC, the PEC is extrapolated to the complete basis set limit by the two-point total-energy extrapolation scheme; and the scalar relativistic correction is included. Scalar relativistic correction calculations are carried out using the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. The spectroscopic parameters (Te, De, Re, ωe, ωexe, ωeye, Be and αe) of two states are calculated. The spectroscopic results are compared in detail with those reported in the previous literature. Excellent agreement is found between the present spectroscopic results and the experimental ones. Using the PECs obtained by the MRCI+Q/Q5+DK calculations, the Bυ and Dυ are calculated for each vibrational state of each electronic state, and their values of the first 30 vibrational states are reported for X1Σ+ and A1Π states of 28Si80Se molecule when J=0. Comparison with the measurements demonstrates that the present vibrational manifolds are both reliable and accurate. They should be good predictions for the future experimental or theoretical research.