In this paper, we present a method of ship size extraction for Sentinel-1 synthetic aperture radar (SAR) images, which is composed of the image processing stage and the regression stage. In order to achieve extraction with high accuracy, considering the data characteristics of Sentinel-1 images, we propose to use the dual-polarization fusion and the nonlinear regression with the gradient boosting. The experiments and analyses on a relatively large data set show that: 1) compared with the existing and related studies, the proposed method achieves an improved performance. The extraction errors are pushed under one pixel, and they are 4.66% (8.80 m) and 7.01% (2.17 m) for length and width, respectively; 2) the dual-polarization information fusion does improve the size extraction accuracy; and 3) the nonlinear regression does exploit the relationship between the influential factors and the size parameters and provide a better performance than the linear regression. The experimental results verify that the proposed design is suitable for ship size extraction in Sentinel-1 SAR images.