Abstract: During the launching process of the railgun, the high temperature air mass outside the muzzle moves to the interior at a speed far higher than the sound speed, which will change the arc shape of the muzzle and cause the arc displacement. This paper makes a numerical calculation of the movement process of the muzzle arc, based on the theory of magneto hydro dynamical (MHD), with a treatment method of potential boundary condition closely related to the electric conductivity of the arc plasma itself, and a three dimensional simulation model of the muzzle position arc is established. The arc motion under the backflow effect is analyzed, and the influence of the arc on the temperature distribution of the railgun inner bore flow field is studied. The simulation results show that the movement of the muzzle arc intensifies the temperature rise in the bore.