The present invention relates to an underwater rock boring apparatus having differential global positioning system receiver and boring method thereof, new boring technology--a satellite navigation device orients the accurate position of a target--is brought to the underwater boring technology.A differential global positioning system (DGPS) receiver is provided at the body of a boring machine that is installed at the central opening of a self elevation platform (SEP) barge, the location of the boring machine is set to concentricity of the target boring position, and the position of the hull can be controlled without any movement of the boring machine. Then, the barge quickly moves to the next target boring location owing to the operation of a hull moving means so that the construction efficiency of the boring work can be enhanced.