With the rapid development of Deep Learning, deep predictive models have been widely applied to improve Software Engineering tasks, such as defect prediction and issue classification, and have achieved remarkable success. They are mostly trained in a supervised manner, which heavily relies on high-quality datasets. Unfortunately, due to the nature and source of software engineering data, the real-world datasets often suffer from the issues of sample mislabelling and class imbalance, thus undermining the effectiveness of deep predictive models in practice. This problem has become a major obstacle for deep learning-based Software Engineering. In this paper, we propose RobustTrainer, the first approach to learning deep predictive models on raw training datasets where the mislabelled samples and the imbalanced classes coexist. RobustTrainer consists of a two-stage training scheme, where the first learns feature representations robust to sample mislabelling and the second builds a classifier robust to class imbalance based on the learned representations in the first stage. We apply RobustTrainer to two popular Software Engineering tasks, i.e., Bug Report Classification and Software Defect Prediction. Evaluation results show that RobustTrainer effectively tackles the mislabelling and class imbalance issues and produces significantly better deep predictive models compared to the other six comparison approaches.