A millisecond laser combined with a nanosecond laser was applied to machining transparent materials. The influences of delay between the two laser pulses on processing efficiencies and modified sizes were studied. In addition, a laser-supported combustion wave (LSCW) was captured during laser irradiation. An optimal delay corresponding to the highest processing efficiency was found for cone-shaped cavities. The modified size as well as the lifetime and intensity of the LSCW increased with the delay decreasing. Thermal cooperation effects of defects, overlapping effects of small modified sites, and thermal radiation from LSCW result in all the phenomena.