Neural architecture search (NAS) has been successfully applied to tasks like image classification and language modeling for finding efficient high-performance network architectures. In ASR field especially end-to-end ASR, the related research is still in its infancy. In this work, we focus on applying NAS on the most popular manually designed model: Conformer, and then propose an efficient ASR model searching method that benefits from the natural advantage of differentiable architecture search (Darts) in reducing computational overheads. We fuse Darts mutator and Conformer blocks to form a complete search space, within which a modified architecture called Darts-Conformer cell is found automatically. The entire searching process on AISHELL-1 dataset costs only 0.7 GPU days. Replacing the Conformer encoder by stacking searched cell, we get an end-to-end ASR model (named as Darts-Conformner) that outperforms the Conformer baseline by 4.7\% on the open-source AISHELL-1 dataset. Besides, we verify the transferability of the architecture searched on a small dataset to a larger 2k-hour dataset. To the best of our knowledge, this is the first successful attempt to apply gradient-based architecture search in the attention-based encoder-decoder ASR model.