Imbalanced classification is widespread in the fields of medical diagnosis, biomedicine, smart city and Internet of Things. The imbalance of data distribution makes traditional classification methods more biased towards majority classes and ignores the importance of minority class. It makes the traditional classification methods ineffective in imbalanced classification. In this paper, a novel imbalance classification method based on deep learning and fuzzy support vector machine is proposed and named as DFSVM. DFSVM first uses a deep neural network to obtain an embedding representation of the data. This deep neural network is trained by using triplet loss to enhance similarities within classes and differences between classes. To alleviate the effects of imbalanced data distribution, oversampling is performed in the embedding space of the data. In this paper, we use an oversampling method based on feature and center distance, which can obtain more diverse new samples and prevent overfitting. To enhance the impact of minority class, we use a fuzzy support vector machine (FSVM) based on cost-sensitive learning as the final classifier. FSVM assigns a higher misclassification cost to minority class samples to improve the classification quality. Experiments were performed on multiple biological datasets and real-world datasets. The experimental results show that DFSVM has achieved promising classification performance.