Potential energy curves (PECs) for the ground electronic state (X4∑) and the three lowest excited electronic states (a2Π, b2∑, A4Π) of NaCmolecule were calculated using the multi-configuration reference single and double excited configuration interactionmethod, including Davidson's corrections for quadruple excitations (MRCI+Q). The equilibrium bond length Re and the vertical excited energy Te were determined directly and the PECs were fitted to an analytical Murrell-Sorbie (MS) potential function to determine the spectroscopic parameters, which were the rotation coupling constant ωe, dissociation energy De, the anharmonic constant ωe Χe, the equilibrium rotation constant Be and Drot, and the vibration-rotation coupling constant αe. These values were also compared and were in agreement with other theoretical and experimental results currently available. It is evident that the X4∑, a2Π, and b2∑ states are bound. We found that in the ground state X4∑, Re was 0.2259 nm, ωe was 431 cm-1, and De was 1.92 eV, while in the excited states a2Πand b2∑, Re and ωe were 0.2447, 0.2369 nm and 329, 335 cm-1, respectively. Te was found to be 1.58 and 1.75 eV and De was 0.71 and 0.42 eV. A4Πis a repulsive excited state when Te is 2.48 eV relative to the ground state. By solving the radial Schrodinger equation of nuclear motion the vibration levels and inertial rotation constant at rotational quantum number J=0 are reported for the X4∑, a2Π, and b2∑ states.