Subgroup discovery is a problem in machine learning and data mining in which the population data is mined to discover interesting subgroups with respect to a target property. The goal of subgroup discovery is to find rules describing subsets of the population. In this paper, a new solving approach is proposed (FDG-SD). The new approach adopts fuzzy rule induction that uses a dynamic programming like algorithm to discover fuzzy subgroups. FDG-SD surpasses disadvantages of existing approaches. It is able to find better solutions for almost half out of 30 UCI machine learning repository datasets based on significance, unusualness, support, confidence and running time quality measures. According to Friedmann test results, the new approach (FDG-SD) is ranked first among mostly used algorithms with respect to significance, unusualness, support and running time quality measures.