Lesion segmentation is one of the crucial steps for computerized dermoscopy image analysis. To accurately extract lesion borders from dermoscopy images, a novel segmentation method based on fully convolutional neural network is proposed in this paper. The designed network contains a low-level trunk followed by two brunches (global brunch and local brunch). The low-level trunk is fine-tuned from VGG16 net. Two brunches with different receptive fields extract global and local features respectively. After the combination of the global and local features, the final segmentation results are obtained through pixel-wise softmax classification. Experiments are conducted on the challenge dataset ISBI 2016. The results demonstrate that our designed network is more adaptive to dermoscopy images, which obtain more accurate lesion borders with good robust than other state-of-the-art methods.