Traditional centralized machine learning uses a large amount of data for model training, which may face some privacy and security problems. On the other hand, federated learning (FL), which focuses on privacy protection, also faces challenges such as core network congestion and limited mobile device (MD) resources. The computation offloading technology of mobile edge computing (MEC) can effectively alleviate these challenges, but it ignores the effect of user mobility and the unpredictable MEC environment. In this paper, we first propose an architecture that combines digital twin (DT) and MEC technology with the FL framework, where the DT network can virtually imitate the statue of physical entities (PEs) and network topology to be used for real-time data analysis and network resource optimization. The computation offloading technology of MEC is used to alleviate resource constraints of MDs and the core network congestion. We further leverage the FL to construct DT models based on PEs’ running data. Then, we jointly optimize the problem of computation offloading and resource allocation to reduce the straggler effect in FL based on the framework. Since the solution of the objective function is a stochastic programming problem, we model a markov decision process (MDP), and use the deep deterministic policy gradient (DDPG) algorithm to solve this objective function. The simulation results prove the feasibility of the proposed scheme, and the scheme can significantly reduce the total cost by about 50% and improve the communication performance compared with baseline schemes.