Multiple sequence alignment is a useful technique for studying molecular evolution and analyzing structure-sequence relationships. Dynamic programming of multiple sequence alignment has been widely used to find an optimal alignment. However, dynamic programming does not allow for certain types of gap costs, and it limits the number of sequences that can be aligned due to its high computational complexity. The focus of this paper is to use simulated annealing as the basis for developing an efficient multiple sequence alignment algorithm. An algorithm called Multiple Sequence Alignment using Simulated Annealing (MSASA) has been developed. The computational complexity of MSASA is significantly reduced by replacing the high-temperature phase of the annealing process by a fast heuristic algorithm. This heuristic algorithm facilitates in minimizing the solution set of the low-temperature phase of the annealing process. Compared to the dynamic programming approach, MSASA can (i) use natural gap costs which can generate better solution, (ii) align more sequences and (iii) take less computation time.