Structural analysis of handwritten characters relies heavily on robust skeletonization of strokes, which has not been solved well by previous thinning methods. This paper presents an effective fully convolutional network (FCN) to extract stroke skeletons for handwritten Chinese characters. We combine the holistically-nested architecture with regressive dense upsampling convolution (rDUC) and recently proposed hybrid dilated convolution (HDC) to generate pixel-level prediction for skeleton extraction. We evaluate our method on character images synthesized from the online handwritten dataset CASIA-OLHWDB and achieve higher accuracy of skeleton pixel detection than traditional thinning algorithms. We also conduct skeleton based character recognition experiments using convolutional neural network (CNN) classifiers on offline/online handwritten datasets, and obtained comparable accuracies with recognition on original character images. This implies the skeletonization loses little shape information.