The low lying electronic states of the FeSi molecule have been investigated by performing complete active space self-consistent field (CASSCF) and multireference single and double excitation configuration interaction (MRSDCI) calculations. Although the classification of the ground state was not established, the results of the MRSDCI calculations suggest that the ground state of FeSi is (3)Delta, and the lowest excited state is (5)Pi whose transition energy is 0.36 eV including the Davidson-type Q correction. The R-e given by MRSDCI with Q correction is 2.23 Angstrom for (3)Delta and 2.19 Angstrom for (5)Pi. The spectroscopic constants and dipole moments of the low lying (5)Delta and (3)Pi states as well as the (3)Delta and (5)Pi states are also evaluated. The bonding nature of FeSi in the (3)Delta state is discussed in comparison with the FeC molecule.