The electromagnetic railgun is a new concept weapon with the hypersonic launch capability. During the railgun launch process, the armature is accelerated along the rails. A complex and high-speed flow field occurs in the muzzle area when the armature leaves the barrel. Meanwhile, the muzzle temperature will be very high because of the secondary arc and friction. In this paper, an analysis of the railgun muzzle fluid flow field after the armature left the barrel is presented, and a three-dimension numerical model for arc plasma is obtained based on the electromagnetic and hydrodynamic equations. The aerodynamic simulation method with moving boundary is adopted to deduce the boundary conditions of the arc model, where the coupling model and the dynamic meshing method are applied. In addition, the backflow phenomenon is considered in the arc model. The distributions of the temperature and the velocity near the muzzle are computed, especially for the dynamic distribution of the arc plasmas. As we can see from the results, the plasma near the muzzle expands outward when the armature leaves the barrel, and most of the plasma will flow back to the bore in a short time. The existence of muzzle plasma may aggravate the erosion and aluminum deposition, which will lead to negative effects on the launcher’s lifetime.