In this paper, picosecond laser drilling of quartz glass is studied. The 532 nm picosecond laser induced ablation threshold of quartz glass is explored and the basic parameters of the picosecond laser processing of glass, including the laser power, repetition rate and processing time, are investigated. From the study, the ablation threshold of quartz glass at picosecond pulse width is concluded to be around 2.01 J/cm2. It is found that the diameter and depth of the holes drilled in quartz glass are proportional to the laser fluence and processing time, but the rate of increase levels off finally. Meanwhile the laser repetition rate also has an important influence on the machining quality. Picosecond laser crack-free processing of quartz glass is achieved by optimizing the laser parameters based on the ablation threshold and the processing rules obtained in our research.