Federated learning (FL) allows multiple clients to collectively train a high-performance global model without sharing their private data. However, the key challenge in federated learning is that the clients have significant statistical heterogeneity among their local data distributions, which would cause inconsistent optimized local models on the clientside. To address this fundamental dilemma, we propose a novel federated learning algorithm with local drift decoupling and correction (FedDC). Our FedDC only introduces lightweight modifications in the local training phase, in which each client utilizes an auxiliary local drift variable to track the gap between the local model parameter and the global model parameters. The key idea of FedDC is to utilize this learned local drift variable to bridge the gap, i.e., conducting consistency in parameter-level. The experiment results and analysis demonstrate that FedDC yields expediting convergence and better performance on various image classification tasks, robust in partial participation settings, non-iid data, and heterogeneous clients.