This paper presents a hybrid algorithm based on using moth-flame optimization (MFO) algorithm with simulated annealing (SA), namely (SA-MFO). The proposed SA-MFO algorithm takes the advantages of both algorithms. It takes the ability to escape from local optima mechanism of SA and fast searching and learning mechanism for guiding the generation of candidate solutions of MFO. The proposed SA-MFO algorithm is applied on 23 unconstrained benchmark functions and four well-known constrained engineering problems. The experimental results show the superiority of the proposed algorithm. Moreover, the performance of SA-MFO is compared with well-known and recent meta-heuristic algorithms. The results show competitive results of SA-MFO concerning MFO and other meta-heuristic algorithms.