Previous ship detection methods for synthetic aperture radar (SAR) images suffer from an extreme variance of ship scale. The problem of large scale variation across ships lies in the heart of ship detection. In this paper, scale-transferrable pyramid network for multi-scale ship detection in SAR images is proposed. We construct a feature pyramid network by lateral connection, and densely connect each feature maps from top to down using scale-transfer layer. Lateral connection injects more semantic information into feature maps with high resolution. Dense scale-transfer connection can expand the resolution of feature maps and explicitly explore information contained in channels. Finally, we can detect multi-scale ships by combining these multi-scale feature maps. Experimental results demonstrate that our network outperforms the state-of-the-art methods.