The growing complexity of software projects requires increasing consideration of their analysis and testing. Identifying defective software entities is essential for software quality assurance and it also improves activities related to software testing. In this study, we developed a novel supervised classification method called HyGRAR for software defect prediction. HyGRAR is a non-linear hybrid model that combines gradual relational association rule mining and artificial neural networks to discriminate between defective and non-defective software entities. Experiments performed based on 10 open-source data sets demonstrated the excellent performance of the HYGRAR classifier. HyGRAR performed better than most of the previously proposed approaches for software defect prediction in performance evaluations using the same data sets.