Face detection of comic characters is a necessary step in most applications, such as comic character retrieval, automatic character classification and comic analysis. However, the existing methods were developed for simple cartoon images or small size comic datasets, and detection performance remains to be improved. In this paper, we propose a Faster R-CNN based method for face detection of comic characters. Our contribution is twofold. First, for the binary classification task of face detection, we empirically find that the sigmoid classifier shows a slightly better performance than the softmax classifier. Second, we build two comic datasets, JC2463 and AEC912, consisting of 3375 comic pages in total for characters face detection evaluation. Experimental results have demonstrated that the proposed method not only performs better than existing methods, but also works for comic images with different drawing styles.