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In this article, we propose a hardware accelerator design using ferroelectric transistor (FeFET)-based hybrid precision synapse (HPS) for deep neural network (DNN) on-chip training. The drain erase scheme for FeFET programming is incorporated for both FeFET HPS design and FeFET buffer design. By using drain erase, high-density FeFET buffers can be integrated onchip to store the intermediate input-output activations and gradients, which reduces the energy consuming off-chip DRAM access. Architectural evaluation results show that the energy efficiency could be improved by 1.2x ~ 2.1x, 3.9x ~ 6.0x compared to the other HPS-based designs and emerging non-volatile memory baselines, respectively. The chip area is reduced by 19% ~ 36% compared with designs using SRAM on-chip buffer even though the capacity of FeFET buffer is increased. Besides, by utilizing drain erase scheme for FeFET programming, the chip area is reduced by 11% ~ 28.5% compared with the designs using body erase scheme. [ABSTRACT FROM AUTHOR]