To study the physical process of a cathode spot jet in vacuum arc discharge with a metal deuteride cathode (TiD), a two-dimensional hydrodynamic model based on three-fluid theory is established in this paper. The ionization and recombination of the plasma are considered in this model. The total current of the cathode spot is set to 2-4 A. The simulation shows that: (1) for Ti ions, there are huge pressure gradients and D-Ti ion collisions (10 13 -10 14 Pa m −1 ) in both the axial and radial direction near the cathode spot region, therefore the plasma jet will expand rapidly in all directions. For D ions, the ion collisions (D-Ti) play an important role in the whole region of the cathode spot jet, resulting in the velocity of a deuterium ionbeing limited to a level close to the velocity of a titanium ion (u i ). (2) Due to the expansion of the cathode spot jet, the ion density decreased rapidly from 10 26 m −3 to 10 22 m −3 . Meanwhile, ion speed quickly reached a level of 10 4 m s −1 at a distance of 2 µm from the cathode spot. (3) When the current of the cathode spot is small (I = 2 A), deuterium ions obtained by the reaction path are significantly less than that obtained by the reaction path. However, with an increase in the cathode spot current, deuterium ions obtained by the two reaction paths are almost the same. (4) Finally, the plasma parameters of the cathode spot jet predicted by our numerical model are in good agreement with the experimental results.