Chart images are widely employed as the intuitive form to express information, which renders them highly valuable. Consequently, there is an urgent demand to develop a watermarking algorithm for copyright protection and leakage prevention of chart images. Nevertheless, existing chart watermarking methods fail to thoroughly consider the chart image’s special characteristics and simply rely on the previous natural image-based watermarking framework. Compared to natural images, the chart image generally exhibits relatively simple layouts and textures, containing fewer complex texture regions that watermarks are typically embedded in. Therefore, the embedding locations of watermarks for different distortions can be relatively dispersed in natural images, while for chart images, watermark embedding regions under various distortion conditions tend to be relatively concentrated and share more overlaps. Inspired by the above special characteristics of chart images, to sufficiently leverage them and design a better framework, this paper proposes C3hartMark, a chart watermarking scheme with consecutive-encoding and concurrent-decoding. Instead of using the combined noise layer as existing methods to ensure multiple robustness, a novel consecutive training framework is introduced in this paper, which efficiently utilizes the overlapping of embedded watermark features in chart images, and simultaneously, mitigates the poor convergence brought by the combined noise layer. During the extraction stage, multiple concurrent decoders are introduced to extract the potential embedded watermarks for different distortions independently. Moreover, we also incorporate two special noise layers, namely Captioning and Fusion, to address the corresponding realistic distortions in chart images, and an agnostic noise layer to accommodate potential channel transmission distortions unknown during training. Through extensive experiments, we demonstrate that with the better visual quality, C3hartMark simultaneously outperforms existing state-of-the-art (SOTA) watermarking methods in terms of robustness, achieving 99.57% extraction accuracy under JPEG compression (QF=60).