In order to improve the drilling efficiency of bit drilling in poor-drillability formation, the authors of this article put forward, a cutting-percussion hybrid bit, the fixed-cutting units and impact-crushing units of which are mutually independent and are able to work in parallel. Through finite element analysis, it is concluded that the impact teeth will degenerate the material and mechanical properties of the rock, and that the polycrystalline diamond compact cutters will remove the pre-damaged rock with relatively low energy consumption, The simulation results show that the maximum axial force and maximum cutting force of rock breaking by punching are reduced, the average axial force is reduced by 34.93 N, 12.1%, and the average tangential force is reduced by 26.09 N, 9.1%, thus improving the rock-breaking efficiency of the bit.Moreover, on the basis of the geometrical and kinematical characteristics of the hybrid bit, geometrical relationships between the teeth and the bit body, as well as the kinematics and kinetics of the teeth, are studied in compound coordinate systems. Furthermore, by programming in MATLAB, the rock-breaking process of the hybrid bit is simulated and the simulation results consist of the bottom-hole profile, cutting area, cutting volume, and cutting force of the cutters, providing the theoretical basis for the research and development of the hybrid bit.