When simulating genome-scale metabolite production using constraint-based metabolic networks, it is often necessary to find gene deletion strategies which lead to growth-coupled production, which means that target metabolites are produced when cell growth is maximized. Existing methods are effective when the number of gene deletions is relatively small, but when the number of required gene deletions exceeds approximately 1% of whole genes, the time required for the calculation is often unfeasible. Therefore, a complementing algorithm that is effective even when the required number of gene deletions is approximately 1% to 5% of whole genes would be helpful because the number of deletable genes in a strain is increasing with advances in genetic engineering technology. In this study, the author developed an algorithm, TrimGdel, which first computes a strategy with many gene deletions that results in growth-coupled production and then gradually reduces the number of gene deletions while ensuring the original production rate and growth rate. The results of the computer experiments showed that TrimGdel can calculate stoichiometrically feasible gene deletion strategies, especially those whose sizes are 1 to 5% of whole genes, which lead to growth-coupled production of many target metabolites, which include useful vitamins such as biotin and pantothenate, for which existing methods could not.