As the main source of the vacuum arc plasma, cathode spots (CSs) play an important role on the behaviors of the vacuum arc. Their characteristics are affected by many factors, especially by the magnetic field. In this paper, the characteristics of the plasma jet from a single CS in vacuum arc under external axial magnetic field (AMF) are studied. A multi-species magneto-hydro-dynamic (MHD) model is established to describe the vacuum arc. The anode temperature is calculated by the anode activity model based on the energy flux obtained from the MHD model. The simulation results indicate that the external AMF has a significant effect on the characteristic of the plasma jet. When the external AMF is high enough, a bright spot appears on the anode surface. This is because with a higher AMF, the contraction of the diffused arc becomes more obvious, leading to a higher energy flux to the anode and thus a higher anode temperature. Then more secondary plasma can be generated near the anode, and the brightness of the ‘anode spot’ increases. During this process, the arc appearance gradually changes from a cone to a dumbbell shape. The appearance of the plasma jet calculated in the model is consistent with the experimental results.