Chart visualizations are essential for data interpretation and communication; however, most charts are only accessible in image format and lack the corresponding data tables and supplementary information, making it difficult to alter their appearance for different application scenarios. To eliminate the need for original underlying data and information to perform chart editing, we propose ChartReformer, a natural language-driven chart image editing solution that directly edits the charts from the input images with the given instruction prompts. The key in this method is that we allow the model to comprehend the chart and reason over the prompt to generate the corresponding underlying data table and visual attributes for new charts, enabling precise edits. Additionally, to generalize ChartReformer, we define and standardize various types of chart editing, covering style, layout, format, and data-centric edits. The experiments show promising results for the natural language-driven chart image editing.