Automatic ultrasound (US) image segmentation is highly desired for improving clinical workflow and diagnostic accuracy. However, the task always has been challenging as the US image has the characteristics of speckle noise, blurred boundary, and inhomogeneous distributions. To solve these problems, this paper proposes a new two-stream network based on feature separation and complementation (FSC-Net) for ultrasound image segmentation. For the feature separation, FSC-Net uses two branches, namely Top-To-Bottom (T2B) and Bottom-To-Top (B2T) streams, to extract global semantic information and local detailed information respectively, and each branch can extract the concerned feature information more effectively. For the feature complementation, FSC-Net performs the interaction between the global semantic information and the local detailed information at each stage gradually, so it can complement the boundary feature of regions of interest (ROIs) in the T2B stream and suppress the noise in the B2T stream timely. We evaluate the proposed method on three publicly available datasets, i.e., UDIAT, BUSIS, and LUSI. The Dice of our FSC-Net in the three datasets are 0.8698, 0.9350, and 0.8972, respectively, which are at least 1.59%, 0.96%, and 3.74% higher than other state-of-the-art ultrasound image segmentation methods.