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Novel category discovery aims at adapting models trained on known categories to novel categories. Previous works only focus on the scenario where known and novel categories are of the same granularity. In this paper, we investigate a new practical scenario called Fine-grained Category Discovery under Coarse-grained supervision (FCDC). FCDC aims at discovering fine-grained categories with only coarse-grained labeled data, which can adapt models to categories of different granularity from known ones and reduce significant labeling cost. It is also a challenging task since supervised training on coarse-grained categories tends to focus on inter-class distance (distance between coarse-grained classes) but ignore intra-class distance (distance between fine-grained sub-classes) which is essential for separating fine-grained categories. Considering most current methods cannot transfer knowledge from coarse-grained level to fine-grained level, we propose a hierarchical weighted self-contrastive network by building a novel weighted self-contrastive module and combining it with supervised learning in a hierarchical manner. Extensive experiments on public datasets show both effectiveness and efficiency of our model over compared methods. Code and data are available at https://github.com/Lackel/Hierarchical_Weighted_SCL.