Federated Learning (FL) has emerged as a de facto machine learning area and received rapid increasing research interests from the community. However, catastrophic forgetting caused by data heterogeneity and partial participation poses distinctive challenges for FL, which are detrimental to the performance. To tackle the problems, we propose a new FL approach (namely GradMA), which takes inspiration from continual learning to simultaneously correct the server-side and worker-side update directions as well as take full advantage of server’s rich computing and memory resources. Furthermore, we elaborate a memory reduction strategy to enable GradMA to accommodate FL with a large scale of workers. We then analyze convergence of GradMA theoretically under the smooth non-convex setting and show that its convergence rate achieves a linear speed up w.r.t the increasing number of sampled active workers. At last, our extensive experiments on various image classification tasks show that GradMA achieves significant performance gains in accuracy and communication efficiency compared to SOTA baselines. We provide our code here: https://github.com/lkyddd/GradMA.