As an extension of the classical Parallel Machine Scheduling Problem (PMSP), Unrelated Parallel Machine Scheduling Problem (UPMSP) is a much substantial issue in the modern manufacturing environment. It has been demonstrated to be a NP-hard problem. This research suggests a hybrid algorithm that combines Matching Theory (MT) and Simulated Annealing (SA) for solving an UPMSP with sequence-dependent setup time aimed at minimizing the total completion time. The hybrid algorithm is based on allocation of works to the best machine that can do it, and the determination of the order in which jobs have to be handled on the machines. The hybridization of MT and SA that integrates the features of these two individual parts is the main innovation aspect of the strategy. MT encourages the convergence, while SA promotes the diversity. Therefore, the designed algorithm can balance the intensification and diversification very well. Some tests were conducted using 16 tests for two problems to assess the efficiency of the suggested algorithm. Furthermore, the execution of the suggested algorithm with that of other meta-heuristic methods was contrasted. The outcome revealed that the performance dimensions of the suggested algorithm overrated those of other techniques.