A pipe connecting device comprises a connecting body including a first tube having a stop jaw at an end thereof and a second tube coupled to the first tube by a fastener and having an opening for insertion of a pipe, wherein a wedge groove is formed in the connecting body and includes rotary corners having a L-shaped cross section and surrounding a circumference of the pipe, rotary wedges each including a rotary part and an extension part, wherein the rotary part is provided in the wedge groove, has a semicircular cross section, and rotates while in tight contact with the rotary corners, and wherein the extension part is formed integrally with the rotary part, has teeth, and contacts the pipe, an elastic member contacting the rotary wedges to transfer a rotational force to the rotary wedges, and a sealing member embedded in the connecting body.