With the purpose of minimizing the makespan of three-machine job shop scheduling problem with intermediate transfer, in this study, a new model was built to perform the makespan minimization, which was proved to be strongly NP-hard. From this model a heuristic algorithm was subsequently derived with a worst-case error bound. The proposed model and derived algorithm were verified through computational experiments carried out on a couple of small size random instances. The results show that the heuristic algorithm possesses a tight worst-case bound of 2. This research presents an approach for obtaining the optimal solutions of the NP-hard problem within a reasonable time.