Recently, the convolutional neural networks (CNNs) show the great power in dealing with various image classification tasks. However, in the task of Chinese character recognition, there is a significant problem in CNN-based classifiers:insufficient generalization ability to recognize the Chinese characters with unfamiliar font styles. We call this problem the Style Overfitting. In the process of a human recognizing Chinese characters with various font styles, the internal skeletons of these characters are important indicators. This paper proposes a novel tool named Skeleton Kernel to capture skeleton features of Chinese characters. And we use it to assist CNN-based classifiers to prevent the Style Overfitting problem. Experimental results prove that our method firmly enhances the generalization ability of CNN-based classifiers. And compared to previous works, our method requires a small training set to achieve relatively better performance.