Road extraction is a process of automatically generating road maps mainly from satellite images. Existing models all target to generate roads from the scratch despite that a large quantity of road maps, though incomplete, are publicly available (e.g. those from OpenStreetMap) and can help with road extraction. In this paper, we propose to conduct road extraction based on satellite images and partial road maps, which is new. We then propose a two-branch Partial to Complete Network (P2CNet) for the task, which has two prominent components: Gated Self-Attention Module (GSAM) and Missing Part (MP) loss. GSAM leverages a channel-wise self-attention module and a gate module to capture long-range semantics, filter out useless information, and better fuse the features from two branches. MP loss is derived from the partial road maps, trying to give more attention to the road pixels that do not exist in partial road maps. Extensive experiments are conducted to demonstrate the effectiveness of our model, e.g. P2CNet achieves state-of-the-art performance with the IoU scores of 70.71% and 75.52%, respectively, on the SpaceNet and OSM datasets.