Addressing the limitations of existing metric-based few-shot fine-grained classification methods, which often neglect task-specific nuances and suffer from inaccurate category descriptions and irrelevant information, we introduce TAFD-Net: a novel Task Adaptive Feature Distribution Network. Our approach innovatively integrates two key components: (1) a task-adaptive embedding module that captures fine-grained features tailored to each task, and (2) an asymmetric metric module that computes similarities between query samples and support categories based on their feature distributions. Through comprehensive experiments on three datasets, TAFD-Net demonstrates superior performance compared to recent incremental learning algorithms, highlighting its effectiveness in accurately describing categories.