Abstract: The highly accurate internally contracted multireference configuration interaction method with the Davidson modification (MRCI+Q) was employed to calculate the potential energy curves (PECs) of the X¹Σ⁺,a³Π and X¹Σ⁺,a³Π electronic states of the BeO molecule. The Dunning’s correlation-consistent basis sets, aug-cc-pV5Z and aug-cc-pVQZ, were used. The effects on the PEC by the core-valence correlation and relativistic corrections were taken into account. The relativistic correction calculations were made using the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z-DK basis set. The core-valence correlation corrections were calculated with an aug-cc-pCVQZ basis set. With the PECs obtained, the spectroscopic parameters(T_e,R_e,ω_e,ω_ex_e,B_e,α_e and D_e) of each state were determined. On the whole, the most accurate spectroscopic parameters of BeO molecule were determined. Based on these PECs, the whole vibrational states of each state of the non-rotating BeO molecule were computed by numerically solving the radial Schrdinger equation of nuclear motion. The vibrational levels and inertial rotation constants were determined when J = 0. Comparison with the available experimental data and other theories showed that the present spectroscopic parameters and molecular constants were more accurate and complete