Software defect prediction (SDP) is designed to assist software testing, which can reasonably allocate test resources to reduce costs and improve development efficiency. In order to improve the prediction performance, researchers have designed many defect-related features for SDP. However, feature redundancy (FR) and irrelevance caused by the increasing dimensions of data will greatly degrade the performance of defect prediction. In order to solve the problems, researchers have proposed various data dimensionality reduction methods. These methods can be simply divided into two categories of methods: feature selection and feature extraction. However, the two categories of methods have their own advantages and limitation. In this paper, we propose a Hybrid Feature Dimensionality Reduction Approach (HFDRA) for SDP, which combines the two different kinds of methods, to improve the performance of SDP. HFDRA approach can be divided into two stages: feature selection and feature extraction. First, HFDRA divides the original features into several feature subsets through a clustering algorithm in the feature selection stage. Then, in the feature extraction stage, kernel principal component analysis (KPCA) is used to reduce the dimensionality of each feature subset. Finally, the reduced-dimensional data is used to build the prediction model. In the empirical study, we use 22 projects from AEEEM, SOFTLAB, MORP, and ReLink as experiment object. In this paper, we first compare our approach with seven baseline methods and three state-of-the-art methods. Then, we analyze the relationship between FR and prediction performance. Experiment results show that our approach outperforms the state-of-the-art data dimensionality reduction methods for defect prediction.