Context: Reliability prediction is critical for software engineers in the current challenging scenario of increased demand for high-quality software. Even though various software reliability prediction models have been established so far, there is always a need for a more accurate model in today's competitive environment for producing high-quality software. Objective: This paper proposes a neuro-fuzzy hybridized method by integrating self-organized- map (SOM) and fuzzy time series (FTS) forecasting for the reliability prediction of a software system. Methodology: In the proposed approach, a well-known supervised clustering algorithm SOM is incorporated with FTS forecasting for developing a hybrid model for software reliability prediction. To validate the proposed approach, an experimental study is done by applying proposed neuro-fuzzy method on a software failure dataset. In addition, a comparative study was conducted for evaluating the performance of the proposed method by comparing it with some of the existing FTS models. Results: Experimental outcomes show that the proposed approach performs better than the existing FTS models. Conclusion: The results show that the proposed approach can be used efficiently in the software industry for software reliability prediction.