Federated learning has been identified as an efficient decentralized training paradigm for scaling the machine learning model training on a large number of devices while guaranteeing the data privacy of the trainers. FedAvg has become a foundational parameter update strategy for federated learning, which has been promising to eliminate the effect of the heterogeneous data across clients and guarantee convergence. However, the synchronization parameter update barriers for each communication round during the training significant time on waiting, slowing down the training procedure. Therefore, recent state-of-the-art solutions propose using semi-asynchronous approaches to mitigate the waiting time cost with guaranteed convergence. Nevertheless, emerging semi-asynchronous approaches are unable to eliminate the waiting time completely. We propose a full asynchronous training paradigm called FedFa, which can guarantee model convergence and eliminate the waiting time completely for federated learning by using a few buffered results on the server for parameter updating. Further, we provide theoretical proof of the convergence rate for our proposed FedFa. Extensive experimental results indicate our approach effectively improves the training performance of federated learning by up to 6x and 4x speedup compared to the state-of-the-art synchronous and semi-asynchronous strategies while retaining high accuracy in both IID and Non-IID scenarios.