Although prototypical network (ProtoNet) has proved to be an effective method for few-shot sound event detection, two problems still exist. Firstly, the small-scaled support set is insufficient so that the class prototypes may not represent the class center accurately. Secondly, the feature extractor is task-agnostic (or class-agnostic): the feature extractor is trained with base-class data and directly applied to unseen-class data. To address these issues, we present a novel mutual learning framework with transductive learning, which aims at iteratively updating the class prototypes and feature extractor. More specifically, we propose to update class prototypes with transductive inference to make the class prototypes as close to the true class center as possible. To make the feature extractor to be task-specific, we propose to use the updated class prototypes to fine-tune the feature extractor. After that, a fine-tuned feature extractor further helps produce better class prototypes. Our method achieves the F-score of 38.4$\%$ on the DCASE 2021 Task 5 evaluation set, which won the first place in the few-shot bioacoustic event detection task of Detection and Classification of Acoustic Scenes and Events (DCASE) 2021 Challenge.