In multi-cell massive multiple-input multiple-output (MIMO) systems, channel estimation is deteriorated by pilot contamination and the effects of pilot contamination become more severe due to hardware impairments. In this paper, we propose a joint pilot design and channel estimation based on deep residual learning in order to mitigate the effects of pilot contamination under the consideration of hardware impairments. We first investigate a conventional linear minimum mean square error (LMMSE) based channel estimator to suppress the interference caused by pilot contamination. After that, a deep learning based pilot design is proposed to minimize the mean square error (MSE) of LMMSE channel estimation, which is utilized to the joint pilot design and channel estimator for transfer learning approach. For the channel estimator, we use a deep residual learning which extracts the features of interference caused by pilot contamination and eliminates them to estimate the channel information. Simulation results demonstrate that the proposed joint pilot design and channel estimation method can effectively reduce the effect of pilot contamination as well as outperforms the conventional approach in multi-cell massive MIMO scenarios. Moreover, the joint pilot design and channel estimation method using transfer learning further enhances the estimation performance when the prior knowledge of pilot contamination cannot be exploited.