Recognizing fine-grained categories remains a challenging task, due to the subtle distinctions among different subordinate categories, which results in the need of abundant annotated samples. To alleviate the data-hungry problem, we consider the problem of learning novel categories from web data with the support of a clean set of base categories, which is referred to as weak-shot learning. In this setting, we propose a method called SimTrans to transfer pairwise semantic similarity from base categories to novel categories. Specifically, we firstly train a similarity net on clean data, and then leverage the transferred similarity to denoise web training data using two simple yet effective strategies. In addition, we apply adversarial loss on similarity net to enhance the transferability of similarity. Comprehensive experiments demonstrate the effectiveness of our weak-shot setting and our SimTrans method.