Potential energy surfaces for the low-lying electronic states of the WC2 molecule have been studied using the complete active space multiconfiguration self-consistent Geld (CASMCSCF) followed by the multireference singles + doubles configuration interaction (MRSDCI) calculations which include up to 3 million configurations. Spin-orbit effects are included through the-relativistic configuration interaction (RCI) method. We find two nearly degenerate B-5(1) and (3)A(2) electronic states for WC2 both of which form stable minima with dissociation energy of 5.21 eV. Equilibrium geometries, energy separations, dipole moments, and the vibrational frequencies of the electronic states are reported. The nature of bonding is discussed using the wave function composition and the Mulliken population analysis. The spin-orbit effects were found to be quite significant.