The two-stage assembly scheduling problem is widely used in industrial and service industries. This study focuses on the two-stage three-machine flow shop assembly problem mixed with a controllable number and sum-of-processing times-based learning effect, in which the job processing time is considered to be a function of the control of the truncation parameters and learning based on the sum of the processing time. However, the truncation function is very limited in the two-stage flow shop assembly scheduling settings. Thus, this study explores a two-stage three-machine flow shop assembly problem with truncated learning to minimize the makespan criterion. To solve the proposed model, we derive several dominance rules, lemmas, and lower bounds applied in the branch-and-bound method. On the other hand, three simulated annealing algorithms are proposed for finding approximate solutions. In both the small and large size number of job situations, the SA algorithm is better than the JS algorithm in this study. All the experimental results of the proposed algorithm are presented on small and large job sizes, respectively.