Many applications arising from areas of economics, finance and engineering are cast into the sum-of-ratios problem. Usually, the problems are on such a large scale that the existing algorithms are naive yet to obtain an optimal solution of the problems. In this study we develop a heuristic algorithm to obtain such a better solution of the sum-of-ratios problem by means of Ant Colony System. The proposed algorithm can be used for designing a globally optimal algorithm with the help of some certain strategy of global search as well. We report numerical experiments of the heuristic algorithm, which indicates that the best function value obtained from our heuristic algorithm is empirically near to the optimal value with a high probability.