Accurate calculation of molecular energy is of great significance for studying molecular spectral properties. In this work, the potential energy curve and rovibrational spectrum (Gν) of the ground state X1∑+ and the excited states a3Π, a'3∑+ and A1Π of carbon monoxide molecule are calculated by the multi-reference configuration interaction method. In the calculation, the core-valence correlation correction (CV) effect and scalar relativistic (SR) effect are included.In order to obtain an accurate energy of molecule, two computational schemes are adopted. In the first scheme, i.e. (m MRCI+Q/CBS(TQ5)+CV+SR), the molecular orbital wavefunction is obtained from the Hartree-Fock self-consistent field method by using the basis set aug-cc-pVnZ. The wavefunction is first calculated by the state-averaged complete active space self-consistent field approach. Then the multi-reference configuration interaction method (MRCI) is adopted to calculate the dynamic correlation energy in the potential energy curve. Finally, we use the basis set cc-pCVQZ and aug-cc-pVQZ to calculate the CV effect and SR effect by the MRCI method. In the second scheme (aug-cc-pwCVnZ-DK (n=T, Q, 5)), the potential energy curves (PECs) of these four electronic states are calculated by the MRCI method whose basis set (aug-cc-pwCVnZ-DK) contains the CV effect and SR effect. Finally, in order to reduce the error caused by the basis set, we extrapolate the basis sets of the two computational schemes to the complete basis set. On the basis of the PECs plotted by the different methods, we obtain the spectroscopic parameters of the X1∑+, a3Π, a'3∑+ and A1Π states of the carbon monoxide by solving the internuclear Schrödinger equations through utilizing the numerical integration program “LEVEL”.In this paper, we calculate the SR effect and the CV effect by using different schemes, and the latter is indispensable for accurately calculating the molecular structure. For the lowest two electronic states, we consider the dependence of the two effects on the calculation of the Gaussian basis group (Method B), and find that the accuracy of the rovibrational spectrum is improved. It can be seen that these electronic states have higher requirements for electronic correlation calculation. For higher electronic states, the electron cloud distribution is relatively loose, and the electronic correlation obtained by a single Gaussian basis group can achieve the corresponding calculation accuracy. Of course, since the calculation of the rovibrational spectra is essentially only the relative energy, the offset effect of the electronic correlation effect of different electronic states is also included here in this paper.