While convolutional neural networks have gained impressive success recently in solving structured prediction problems such as semantic segmentation, it remains a challenge to differentiate individual object instances in the scene. Instance segmentation is very important in a variety of applications, such as autonomous driving, image captioning, and visual question answering. Techniques that combine large graphical models with low-level vision have been proposed to address this problem; however, we propose an end-to-end recurrent neural network (RNN) architecture with an attention mechanism to model a human-like counting process, and produce detailed instance segmentations. The network is jointly trained to sequentially produce regions of interest as well as a dominant object segmentation within each region. The proposed model achieves competitive results on the CVPPP, KITTI, and Cityscapes datasets.