The invention discloses a continuous cyclic drilling process applicable to air drilling. The process includes the steps: a valve plate A (7) of a center check valve (2) is provided with a sealing portion A, a valve body A (6) is provided with a sealing match portion A, a valve plate B (12) of a lateral vertical check valve (3) is provided with a sealing portion B, and a valve body B (11) is provided with a sealing match portion B. During normal drilling operation, a pipeline A is connected with the center check valve (2) to supply air to a drill stem; and when the drill stem needs to be demounted, a pipeline B is connected to the lateral vertical check valve (3) to supply air to the drill stem. The continuous cyclic drilling process applicable to air drilling has the advantages that equivalent cycling density of circulation air of a well can be effectively controlled, and stability in well pressure can be effectively maintained. Drilling time is shortened, and the continuous cyclic drilling process applicable to air drilling is significant to reduction of drilling cost.