Deep learning has significantly improved the precision of instance segmentation with abundant labeled data. However, in many areas like medical and manufacturing, collecting sufficient data is extremely hard and labeling this data requires high professional skills. We follow this motivation and propose a new task set named zero-shot instance segmentation (ZSI). In the training phase of ZSI, the model is trained with seen data, while in the testing phase, it is used to segment all seen and unseen instances. We first formulate the ZSI task and propose a method to tackle the challenge, which consists of Zero-shot Detector, Semantic Mask Head, Background Aware RPN and Synchronized Background Strategy. We present a new benchmark for zero-shot instance segmentation based on the MS-COCO dataset. The extensive empirical results in this benchmark show that our method not only surpasses the state-of-the-art results in zero-shot object detection task but also achieves promising performance on ZSI. Our approach will serve as a solid baseline and facilitate future research in zero-shot instance segmentation. Code available at ZSI.