The cross section geometry of a conductor is an important factor in affecting the corona discharges of DC transmission line. Therefore

it is of great significance to study the effects of cross section structures on the corona discharge characteristics for the selection of conductor specification in HV transmission line. In this paper

a two-dimensional（2 D） plasma hybrid model to simulate the DC positive corona discharge on conductors with different cross sections is first established by using the method of fluid-chemistry kinetics. Then

the electron density and electric field intensity of circular conductor and aluminum conductor steel reinforced（ACSR） are numerically investigated under different discharge time. Moreover

the influences of the number of outer strands for conductors on the corona discharge performance are also discussed. Research results show that the electron density around the ACSR is higher than that around the circular conductor at the initial discharge stage. But the electron density around conductors with different cross sections negligibly varies in the phases of streamer. The electric field intensity of ACSR is significantly higher than that of circular conductor at the initial discharge. The difference of electric field intensity between two conductors is decreasing with the development of discharge time. The electric field and electron density will decrease with increasing the number of outer strands for conductors. It is worth noting that the corona characteristic of the ACSR is close to the circular conductor when the number of strand reaches a certain value.