Machine learning has been widely adopted for medical image analysis in recent years given its promising performance in image segmentation and classification tasks. The success of machine learning, in particular supervised learning, depends on the availability of manually annotated datasets. For medical imaging applications, such annotated datasets are not easy to acquire, it takes a substantial amount of time and resource to curate an annotated medical image set. In this paper, we propose an efficient annotation framework for brain MR images that can suggest informative sample images for human experts to annotate. We evaluate the framework on two different brain image analysis tasks, namely brain tumour segmentation and whole brain segmentation. Experiments show that for brain tumour segmentation task on the BraTS 2019 dataset, training a segmentation model with only 7% suggestively annotated image samples can achieve a performance comparable to that of training on the full dataset. For whole brain segmentation on the MALC dataset, training with 42% suggestively annotated image samples can achieve a comparable performance to training on the full dataset. The proposed framework demonstrates a promising way to save manual annotation cost and improve data efficiency in medical imaging applications.