A bucket attaching structure of a construction machine and a construction machine including a fixed jaw portion attached to a distal end portion of an operation arm and a movable jaw portion attached to a distal end portion of a piston through a bucket link. The fixed jaw portion and the movable jaw portion are each partially open and each include a semicircular arc-shaped engagement portion that corresponds to an outer peripheral surface of a corresponding bucket connecting pin. The bucket attaching structure of a construction machine and the construction machine include semicircular arc-shaped closure portions that each support the bucket connecting pins together with the semicircular arc-shaped engagement portions by, after engaging each semicircular arc-shaped engagement portion with the corresponding connecting pin, closing a partially open side of the corresponding semicircular arc-shaped engagement portion of the fixed jaw portion and that of the movable jaw portion.