Abstract: In a vacuum arc, when there is a composite magnetic field or a special electrode structure, the cathode jet usually inclines. By simulating and analyzing the formation and development of cathode spots in this case, it is helpful to understand the mechanism of cathode erosion under inclined cathode jet. Therefore, we proposed a three-dimensional asymmetric model to study the formation and development of cathode spots under inclined cathode jet at different angles in a vacuum arc. The model includes mass, momentum, heat transfer (energy), current continuity and potential equations. Peak energy flux density, peak pressure and current value are adopted as external parameters. According to the simulation results, we compared the morphology of the cathode spot crater, the temperature of the cathode, the velocity of the liquid metal, and the current density inside the cathode under inclined cathode jet at different angles α. Results show that the smaller α between cathode jet and electrode facilitates the formation of longer major axis of the elliptical spot crater. When α is 30 degrees, the metal droplets appear more in the direction opposite to the energy inflow direction at first. As the electrode is increasingly melted, a barrier is naturally formed to prevent the metal droplets from that side, and the subsequent metal droplets appear more in the direction of energy inflow. The maximum value of the cathode temperature and the liquid metal velocity increases when α becomes smaller. This is because the smaller α leads to the larger contact area between the energy flux and the cathode metal. The simulation results are in good agreement with other researchers' results.