Text-to-image diffusion models can generate diverse, high-fidelity images based on user-provided text prompts. Recent research has extended these models to support text-guided image editing. While text guidance is an intuitive editing interface for users, it often fails to ensure the precise concept conveyed by users. To address this issue, we propose Custom-Edit, in which we (i) customize a diffusion model with a few reference images and then (ii) perform text-guided editing. Our key discovery is that customizing only language-relevant parameters with augmented prompts improves reference similarity significantly while maintaining source similarity. Moreover, we provide our recipe for each customization and editing process. We compare popular customization methods and validate our findings on two editing methods using various datasets.