Potential energy curves (PECs) for the ground electronic state, (X-4 Sigma) and the three lowest excited electronic states (a(2)Pi, b(2)Sigma, A(4)Pi) of NaC molecule were calculated using the multi-configuration reference single and double excited configuration interaction method, including Davidson's corrections for quadruple excitations (MRCI+Q). The equilibrium bond length R-e and the vertical excited energy T-e 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 omega(e), dissociation energy D-e, the anharmonic constant omega(e)chi(e), the equilibrium rotation constant B-e and D-rot, and the vibration-rotation coupling constant alpha(e). These values were also compared and were in agreement with other theoretical and experimental results currently available. It is evident that the X-4 Sigma, a(2)Pi and b(2)Sigma states are bound. We found that in the ground state X-4 Sigma, R-e was 0.2259 nm, omega(e) was 431 cm(-1). and D-e was 1.92 eV, while in the excited states a(2)Pi and b(2)Sigma. R-e and omega(e) were 0.2447, 0.2369 nm and 329, 335 cm(-1), respectively. T-e was found to be 1.58 and 1.75 eV and D-e was 0.71 and 0.42 eV. A(4)Pi is a repulsive excited state when T-e 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 X-4 Sigma, a(2)Pi, and b(2)Sigma states.