In recent years, in order to balance performance and cost, hybrid power modules of Si IGBT and SiC Schottky diodes (SiC SBD) have appeared. Since SiC SBDs have almost no reverse recovery, the turn-on losses of hybrid power modules are significantly reduced compared to all-Si IGBT. However, due to the parasitic capacitance of the SiC diode and the existence of the parasitic inductance of the loop, when the IGBT is turned on (the SiC diode is turned off), the hybrid power module will generate switching oscillations, which will affect the normal operation of the system.In order to suppress the switching oscillation of the hybrid power module and reduce the electromagnetic interference of the power module, this paper adopts the stacked DBC hybrid package to reduce the parasitic inductance that causes the high-frequency oscillation of the hybrid power module, and introduces a damping circuit in the upper-layer DBC to absorb oscillating current. The results show that the use of the stacked DBC hybrid package can significantly reduce parasitic inductances that cause switching oscillations in power modules. At the same time, the reduction of the parasitic inductances and the introduction of the damping circuit can effectively suppress the switching oscillation of the hybrid power module, and will not cause more additional losses due to the introduction of the damping resistance. This work provides a reference scheme for suppressing switching oscillations of hybrid power modules, ensuring stable operation and efficiency advantages of hybrid devices.