Manufacturing systems are constrained by one or more bottlenecks. Reducing bottlenecks improves the entire system. Finding bottlenecks, however, is a difficult task. In this study, a new bottleneck detection method based on theory of constrains and sensitivity analysis is presented to overcome the disadvantages of existing bottleneck identification methods for a job shop. First, a bottleneck index matrix is obtained by examining the sensitivity of system production performance to the capacity of each machine. Technique for order preference by similarity to ideal solution is then employed to calculate the comprehensive bottleneck index of each machine. Based on the calculation result, bottleneck machine clusters under different hierarchies are obtained through hierarchical cluster analysis. The designed identification approach, as a prior-to-run method, can identify bottleneck machine clusters under different hierarchies before the overall system circulation, thereby providing good guidance for subsequent production optimization. Finally, a set of job-shop scheduling problem benchmarks with different scales is selected for comparison between the proposed approach and existing approaches, such as, the shifting bottleneck detection method, the bottleneck detection method based on orthogonal experiment, and the bottleneck cluster identification method. By comparison, the proposed approach is proven to be credible and superior.