The invention discloses an automatic drilling tapping machine which comprises a base, a support, a horizontal pneumatic mechanism, a supporting platform, a positioning clamp, a vertical pneumatic mechanism, a drilling machine and a control mechanism. The base is provided with the support, the horizontal pneumatic mechanism and the supporting platform are arranged on the middle portion of the support, the horizontal pneumatic mechanism is provided with the positioning clamp, the vertical pneumatic mechanism is arranged at the upper end of the support, the drilling machine is arranged on the vertical pneumatic mechanism, and the control mechanism is connected with and controls the horizontal pneumatic mechanism and the vertical pneumatic mechanism. The invention further discloses a working method of the automatic drilling tapping machine. An automatic control system is adopted for avoiding the current condition of manual operation, the working content is simplified, manual cost is reduced, comprehensive automation is achieved, and the working efficiency and the safety are improved; supporting plane modularization is carried out so that the machine can be suitable for plates with different sizes and different space shapes, the using scope of the equipment is enlarged, and the automatic drilling tapping machine better meets the enterprise need.