Recently, many researchers have made remarkable achievements in the field of artistic font synthesis, with impressive glyph style and effect style in the results. However, due to less exploration in style disentanglement, it is difficult for existing methods to envision a kind of unseen style (glyph-effect) compositions of artistic font, and thus can only learn the seen style compositions. To solve this problem, we propose a novel compositional zero-shot artistic font synthesis gan (CAFS-GAN), which allows the synthesis of unseen style compositions by exploring the visual independence and joint compatibility of encoding semantics between glyph and effect. Specifically, we propose two contrast-based style encoders to achieve style disentanglement due to glyph and effect intertwining in the image. Meanwhile, to preserve more glyph and effect detail, we propose a generator based on hierarchical dual styles AdaIN to reorganize content-styles representations from structure to texture gradually. Extensive experiments demonstrate the superiority of our model in generating high-quality artistic font images with unseen style compositions against other state-of-the-art methods. The source code and data is available at moonlight03.github.io/CAFS-GAN/.