The prediction of bug types provides useful insights into the software maintenance process. It can improve the efficiency of software testing and help developers adopt corresponding strategies to fix bugs before releasing software projects. Typically, the prediction tasks are performed through machine learning classifiers, which rely heavily on labeled data. However, for a software project that has insufficient labeled data, it is difficult to train the classification model for predicting bug types. Although labeled data of other projects can be used as training data, the results of the cross-project prediction are often poor. To solve this problem, this paper proposes a cross-project bug type prediction framework based on transfer learning. Transfer learning breaks the assumption of traditional machine learning methods that the training set and the test set should follow the same distribution. Our experiments show that the results of cross-project bug type prediction have significant improvement by adopting transfer learning. In addition, we have studied the factors that influence the prediction results, including different pairs of source and target projects, and the number of bug reports in the source project.