Cathode spot (CS), as the main source of interelectrode plasma in vacuum arc, whose characteristics are affected by many factors, of which the magnetic field is the most important one, plays an important role on the behaviors of vacuum arc. In this paper, the characteristics of the plasma jet of each single CS in vacuum arc under axial magnetic field (AMF) were studied. The simulation results indicate that the external AMF has a significant effect on the characteristic of the plasma jet of CS in vacuum arc. In this paper, first, in order to model and simulate the vacuum arc, a multi-species magneto-hydro-dynamic (MHD) model of vacuum arc was established. Second, the model of anode melting and evaporation were interacted with the first simulation. Simulation results indicate that with the strengthening of the external AMF, a bright "spot" appears on the anode surface. This is mainly due to that with the strengthening of the external AMF, the contraction of the diffused arc become more obvious, and the energy flow density injected into the anode increases, which resulted in the anode temperature rising and the sputtering of anode atoms increasing. Therefore, generation of secondary plasma near the anode area increases, and the brightness of the anode "spot" increases. During this process, the arc appearance gradually changed from a cone to a dumbbell shape. Finally, the appearance of the jet calculated in the model is consistent with the experimental data.