In the present work all electron ab initio multiconfiguration self-consistent-held (CASSCF) and multireference configuration interaction (MRCI) calculations have been carried out to determine the low-lying electronic states of the molecule MoC. The relativistic corrections for the one electron Darwin contact term and the relativistic mass-velocity correction have been determined in perturbation calculations. The electronic ground state is predicted as (3) Sigma(-). The spectroscopic constants for the (3) Sigma(-) electronic ground state and eight low-lying excited states have been derived by solving the Schrodinger equation for the nuclear motion numerically. Based on the results of the CASSCF calculations the (3) Sigma(-) ground state of MoC is separated from the excited states (3) Delta, (5) Sigma-, (1) Sigma, (1) Delta, (5) Pi, (1) Sigma(+), and (3) Pi by transition energies of 4500, 6178, 7207, 9312, 10 228, 11 639, and 16 864 cm(-1), respectively. The transition energy between the (3) Sigma(-) ground state and the (3) Pi state as derived in the MRCI calculations is 15 484 cm(-1). For the (3) Sigma(-) ground state the equilibrium distance has been determined as 1.688 Angstrom, and the vibrational frequency as 997 cm(-1). The chemical bond in the (3) Sigma(-) electronic ground state has triple bond character due to the formation of delocalized bonding rr and a orbitals. The chemical bond in the MoC molecule is polar with charge transfer from Mo to C, giving rise to a dipole moment of 6.15 D at 3.15 a.u. in the (3) Sigma(-) ground state.