The joint training framework for speech enhancement and recognition methods have obtained quite good performances for robust end-to-end automatic speech recognition (ASR). However, these methods only utilize the enhanced feature as the input of the speech recognition component, which are affected by the speech distortion problem. In order to address this problem, this paper proposes a gated recurrent fusion (GRF) method with joint training framework for robust end-to-end ASR. The GRF algorithm is used to dynamically combine the noisy and enhanced features. Therefore, the GRF can not only remove the noise signals from the enhanced features, but also learn the raw fine structures from the noisy features so that it can alleviate the speech distortion. The proposed method consists of speech enhancement, GRF and speech recognition. Firstly, the mask based speech enhancement network is applied to enhance the input speech. Secondly, the GRF is applied to address the speech distortion problem. Thirdly, to improve the performance of ASR, the state-of-the-art speech transformer algorithm is used as the speech recognition component. Finally, the joint training framework is utilized to optimize these three components, simultaneously. Our experiments are conducted on an open-source Mandarin speech corpus called AISHELL-1. Experimental results show that the proposed method achieves the relative character error rate (CER) reduction of 10.04\% over the conventional joint enhancement and transformer method only using the enhanced features. Especially for the low signal-to-noise ratio (0 dB), our proposed method can achieves better performances with 12.67\% CER reduction, which suggests the potential of our proposed method.