A cutting tool carrying device includes a carrying member having one or more compartments formed in an outer peripheral portion each for receiving a base member, and a follower slidably engaged into each of the base members for supporting a cutting member. An adjusting device may adjust the follower relative to the base member to partially extend the cutting member out of the outer peripheral portion of the carrying member for suitably machining the work pieces. A pressing device may be slidably attached to the base member for forcing the cutting member to the base member and for allowing the cutting member to be adjusted relative to the base member and the carrying member to the suitable positions.