It is important to identify DNA motifs in promoter regions to understand the mechanism of gene regulation. Computational approaches for finding DNA motifs are well recognized as useful tools to biologists, which greatly help in saving experimental time and cost in wet laboratories. Self-organizing maps (SOMs), as a powerful clustering tool, have demonstrated good potential for problem solving. However, the current SOM-based motif discovery algorithms unfairly treat data samples lying around the cluster boundaries by assigning them to one of the nodes, which may result in unreliable system performance. This paper aims to develop a robust framework for discovering DNA motifs, where fuzzy SOMs, with an integration of fuzzy c-means membership functions and a standard batch-learning scheme, are employed to extract putative motifs with varying length in a recursive manner. Experimental results on eight real datasets show that our proposed algorithm outperforms the other searching tools such as SOMBRERO, SOMEA, MEME, AlignACE, and WEEDER in terms of the F-measure and algorithm reliability. It is observed that a remarkable 24.6% improvement can be achieved compared to the state-of-the-art SOMBRERO. Furthermore, our algorithm can produce a 20% and 6.6% improvement over SOMBRERO and SOMEA, respectively, in finding multiple motifs on five artificial datasets.