Although deep neural networks have achieved amazing results on instance segmentation, they are still ill-equipped when they are required to learn new tasks incrementally. Concretely, they suffer from “catastrophic forgetting”, an abrupt degradation of performance on old classes with the initial training data missing. Moreover, they are subjected to a negative transfer problem on new classes, which renders the model unable to update its knowledge while preserving the previous knowledge. To address these problems, we propose an incremental instance segmentation method that consists of three networks: Former Teacher Network (FTN), Current Student Network (CSN) and Current Teacher Network (CTN). Specifically, FTN supervises CSN to preserve the previous knowledge, and CTN supervises CSN to adapt to new classes. The supervision of two teacher networks is achieved by a distillation loss function for instances, bounding boxes, and classes. In addition, we adjust the supervision weights of different teacher networks to balance between the knowledge preservation for former classes and the adaption to new classes. Extensive experimental results on PASCAL 2012 SBD and COCO datasets show the effectiveness of the proposed method.