In this paper the corona discharge in SF$_{6}$ gas used as insulating material in lots o high voltage equipment, is simulated by finite element method with Flux-Corrected Transport(FCT) method. By application of proposed method the negative corona discharge characteristics in needle to plane electrode is analyzed with time step. For the accuracy of analysis the secondary electron emission by photon and ion are also considered as well as the accuracy of analysis the secondary electron emission by photon and ion are also considered as well as townsend first ionization and electron attachment. The calculated results show that the electric field intensity between anode and ion group is decreased as times go-by according to field distortion by those space charge. Accordingly the electron density is decreased strongly by the attatchment effect of SF6 gas so that the corona discharge becomes extinguished abruptly.y.