This paper proposes a Region-based Convolutional Recurrent Neural Network (R-CRNN) for audio event detection (AED). The proposed network is inspired by Faster-RCNN, a well known region-based convolutional network framework for visual object detection. Different from the original Faster-RCNN, a recurrent layer is added on top of the convolutional network to capture the long-term temporal context from the extracted high level features. While most of the previous works on AED generate predictions at frame level first, and then use post-processing to predict the onset/offset timestamps of events from a probability sequence; the proposed method generates predictions at event level directly and can be trained end-to-end with a multitask loss, which optimizes the classification and localization of audio events simultaneously. The proposed method is tested on DCASE 2017 Challenge dataset. To the best of our knowledge, R-CRNN is the best performing single-model method among all methods without using ensembles both on development and evaluation sets. Compared to the other region-based network for AED (R-FCN) with an event-based error rate (ER) of 0.18 on the development set, our method reduced the ER to half.