Large-scale contrastive vision-language pre-trained models provide the zero-shot model achieving competitive performance across a range of image classification tasks without requiring training on downstream data. Recent works have confirmed that while additional fine-tuning of the zero-shot model on the reference data results in enhanced downstream performance, it compromises the model's robustness against distribution shifts. Our investigation begins by examining the conditions required to achieve the goals of robust fine-tuning, employing descriptions based on feature distortion theory and joint energy-based models. Subsequently, we propose a novel robust fine-tuning algorithm, Lipsum-FT, that effectively utilizes the language modeling aspect of the vision-language pre-trained models. Extensive experiments conducted on distribution shift scenarios in DomainNet and ImageNet confirm the superiority of our proposed Lipsum-FT approach over existing robust fine-tuning methods.