Quadratic configuration interaction method including single and duble substitutions has been used to optimize the possible ground-state structures of B2C and BC2 molecules with the 6-311++G(d, f) and 6-311G(df, pd) basis set. The results show that the ground state of B2C molecule is of C2v symmetry and of 1A1 state, the ground state of BC2 molecule is of Cs symmetry and of 2A′ state. And the equilibrium geometry, dissociation energy, harmonic frequency and force constant have been calculated. The potential energy functions of B2C and BC2 have been derived from the many-body expansion theory. The potential energy functions describe correctly the configurations and the dissociation energies of the two ground-state molecules. Molecular reaction kinetics of B+BC→B2C and B+CC→BC2 based on the potential energy functions is discussed briefly.