We study the federated optimization problem from a dual perspective and propose a new algorithm termed federated dual coordinate descent (FedDCD), which is based on a type of coordinate descent method developed by Necora et al.~\emph{[Journal of Optimization Theory and Applications, 2017]}. Additionally, we enhance the FedDCD method with inexact gradient oracles and Nesterov’s acceleration. We demonstrate theoretically that our proposed approach achieves better convergence rates than the state-of-the-art primal federated optimization algorithms under certain situations. Numerical experiments on real-world datasets support our analysis.