Recently, an increasing number of few-shot image classification methods have been proposed, and they aim at seeking a learning paradigm to train a high-performance classification model with limited labeled samples. However, the neglect of part-level relationships causes few-shot methods to struggle to distinguish between closely similar subcategories, which makes it difficult for them to solve the fine-grained image classification problem. To tackle this challenging task, this paper proposes a fine-grained few-shot image classification method that exploits both intra-part and inter-part relationships among different samples. To establish comprehensive relationships, we first extract multiple discriminative descriptors from the input image, representing its different parts. Then, we propose to define the metric spaces by interpolating intra-part relationships, which can help the model adaptively find clear boundaries for these confusing classes. Finally, since the unlabeled image has high similarities to all classes, we project these similarities into a high-dimension space according to the inter-part relationship and interpolate a parameterized classifier to discover the subtle differences among these similar classes. To evaluate our proposed method, we conduct extensive experiments on various fine-grained datasets. Without any pre-train/fine-tuning process, our approach clearly outperforms previous few-shot learning methods, which demonstrates the effectiveness of our approach.