Bottleneck stage and reentrance often exist in real-life manufacturing processes; however, the previous research rarely addresses these two processing conditions in a scheduling problem. In this study, a reentrant hybrid flow shop scheduling problem (RHFSP) with a bottleneck stage is considered, and an elite-class teaching-learning-based optimization (ETLBO) algorithm is proposed to minimize maximum completion time. To produce high-quality solutions, teachers are divided into formal ones and substitute ones, and multiple classes are formed. The teacher phase is composed of teacher competition and teacher teaching. The learner phase is replaced with a reinforcement search of the elite class. Adaptive adjustment on teachers and classes is established based on class quality, which is determined by the number of elite solutions in class. Numerous experimental results demonstrate the effectiveness of new strategies, and ETLBO has a significant advantage in solving the considered RHFSP.