The potential energy curves (PECs) for the ground electronic state X4Σ-and five low-lying excited electronic states (a2Π, b2Δ, c2Σ-, d2Σ+, A4Π) of LiC have been calculated using the multiconfiguration reference configuration interaction method including Davidson correction (MRCI+Q). And PECs were fitted to analytical Murrell-Sorbie potential function to deduce the spectroscopic parameters of equilibrium bond length Re, rotation coupling constant ωe, anharmonic constant ωeχe, equilibrium rotation constant Be and vibration-rotation coupling constant αe. Those values were also compared with the other results currently available. By solving the radial Schrdinger equation of nuclear motion, the vibration levels, inertial rotation constant and six centrifugal distortion constants (Dν, Hν, Lν, Mν,Nν,and Oν) are reported for the first time.