The invention provides a drainage borehole plugging device and a drainage borehole plugging method. The device comprises a drainage pipe and an elastic borehole plugging capsule. One end of the drainage pipe is inserted into a gas drainage borehole. The elastic borehole plugging capsule is fixedly sheathed on the outer wall of the middle part of the drainage pipe. The two ends of the elastic borehole plugging capsule are hermetically fixed with the outer wall of the drainage pipe. A chamber is formed between the middle part of the elastic borehole plugging capsule and the outer wall surface of the drainage pipe. A grout injection port and a grout outlet are respectively arranged at the two ends of the chamber body, wherein the grout injection port is arranged at one end adjacent to the mouth of the drainage borehole and the grout outlet is arranged at one end far away from the mouth of the drainage borehole. The drainage borehole plugging device and the drainage borehole plugging method provided by the invention have the advantages that since grout injection for plugging is implemented after the elastic borehole plugging capsule is expanded by using grout injection pressure and the functions of plugging and grout injection are integrated in the same device, the plugging and grout injection process is simplified, the air leakage is reduced through elastic sealing of the elastic borehole plugging capsule and the plugging effect is better.