Federated learning (FL) has shown promising results on training machine learning models with privacy preservation. However, for large models with over 100 million parameters, the training resource requirement becomes an obstacle for FL because common devices do not have enough memory and computation power to finish the FL tasks. Although efficient training methods have been proposed, it is still a challenge to train the large models like Conformer based ASR. This paper presents a systematic solution to train the full-size ASR models of 130M parameters with FL. To our knowledge, this is the first real-world FL application of the Conformer model, which is also the largest model ever trained with FL so far. And this is the first paper showing FL can improve the ASR model quality with a set of proposed methods to refine the quality of data and labels of clients. We demonstrate both the training efficiency and the model quality improvement in real-world experiments.