White matter hyperintensity (WMH) is associated with various aging and neurodegenerative diseases. In this paper, we proposed and validated a fully automatic system which integrated classical image processing and deep neural network for segmenting WMH from fluid attenuation inversion recovery (FLAIR) and T1-weighed magnetic resonance (MR) images. A novel skip connection U-net (SC U-net) was proposed and compared with the classical U-net. Experiments were performed on a dataset of 60 images, acquired from three different scanners. Validation analysis and cross-scanner testing were conducted. Compared with U-net, the proposed SC U-net had a faster convergence and higher segmentation accuracy. The software environment and models of the proposed system were made publicly accessible at Dockerhub.