A steel bar connecting structure is disclosed. The steel bar connecting structure includes a connecting sleeve having on an inner circumference thereof an internal threaded part, and a steel bar having an external threaded part which engages with the internal threaded part. The steel bar is inserted into the connecting sleeve. Each of the internal threaded part and the external threaded part is formed such that a crest of each of threads thereof is cut. Thereby, when the steel bar is strongly coupled to the connecting sleeve, a neighboring crest and root of the internal threaded part and the external threaded part are not in contact with each other, whereas inclined flanks of the threads of the internal threaded part and the external threaded part are in close contact with each other.