Dongba characters are ancient ideographic scripts with abstract expressions that differ greatly from modern Chinese characters; directly applying existing methods cannot achieve the font style transfer of Dongba characters. This paper proposes an Attention-based Font style transfer Generative Adversarial Network (AFGAN) method. Based on the characteristics of Dongba character images, two core modules are set up in the proposed AFGAN, namely void constraint and font stroke constraint. In addition, in order to enhance the feature learning ability of the network and improve the style transfer effect, the Convolutional Block Attention Module (CBAM) mechanism is added in the down-sampling stage to help the network better adapt to input font images with different styles. The quantitative and qualitative analyses of the generated font and the real font were conducted by consulting with professional artists based on the newly built small seal script, slender gold script, and Dongba character dataset, and the styles of the small seal script and slender gold script were transferred to Dongba characters. The results indicate that the proposed AFGAN method has advantages in evaluation indexes and visual quality compared to existing networks. At the same time, this method can effectively learn the style features of small seal script and slender gold script, and transfer them to Dongba characters, indicating the effectiveness of this method.