The possibility of using a two-pulse laser action consisting of a pulse of the free-running pulse followed by the Q-switched pulse in the processes of laser drilling in alumina ceramics is considered. A diagram of a laser machine for implementing the proposed processing method and the method for determining the energy required to form the through hole and the drilling time are presented. For thermal exposure, pulsed radiation of Nd:YAG of the laser operating in the free-running mode (pulse duration 0.5 ms, energy up to 0.3 J) was used. The Q-switched pulse was generated using a second Nd:YAG laser (pulse duration 25–30 ns, energy up to 0.03 J). The laser radiation was focused on the surface of the material at one point. The time between the start of generation of the first and second lasers varied in the range of 0–1000 μs. The optimal delay time for the start of the generation of the second laser relative to the first was determined experimentally. The obtained results showed that the combination of the free-running pulse and the Q-switched pulse can significantly increase the efficiency of laser machining of ceramics and improve the hole quality. This scheme turned out to be promising for optimizing parameters of the process of laser drilling in thin-sheet alumina ceramics. The obtained results obtained have great potential in the field of precision laser machining of ceramics.