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Fine-grained classification and counting of bone marrow erythroid cells are vital for evaluating the health status and formulating therapeutic schedules for leukemia or hematopathy. Due to the subtle visual differences between different types of erythroid cells, it is challenging to apply existing image-based deep learning models for fine-grained erythroid cell classification. Moreover, there is no large open-source datasets on erythroid cells to support the model training. In this paper, we introduce BMEC (Bone Morrow Erythroid Cells), the first large fine-grained image dataset of erythroid cells, to facilitate more deep learning research on erythroid cells. BMEC contains 5,666 images of individual erythroid cells, each of which is extracted from the bone marrow erythroid cell smears and professionally annotated to one of the four types of erythroid cells. To distinguish the erythroid cells, one key indicator is the cell shape which is closely related to the cell growth and maturation. Therefore, we design a novel shape-aware image classification network for fine-grained erythroid cell classification. The shape feature is extracted from the shape mask image and aggregated to the raw image feature with a shape attention module. With the shape-attended image feature, our network achieved superior classification performance (81.12\% top-1 accuracy) on the BMEC dataset comparing to the baseline methods. Ablation studies also demonstrate the effectiveness of incorporating the shape information for the fine-grained cell classification. To further verify the generalizability of our method, we tested our network on two additional public white blood cells (WBC) datasets and the results show our shape-aware method can generally outperform recent state-of-the-art works on classifying the WBC. The code and BMEC dataset can be found on https://github.com/wangye8899/BMEC.