Federated learning (FL) has emerged as a promising collaboration paradigm by enabling a multitude of parties to construct a joint model without exposing their private training data. Three main challenges in FL are efficiency, privacy, and robustness. The recently proposed SIGNSGD with majority vote shows a promising direction to deal with efficiency and Byzantine robustness. However, there is no guarantee that SIGNSGD is privacy-preserving. In this paper, we bridge this gap by presenting an improved method called DP-SIGNSGD, which can meet all the aforementioned properties. We further propose an error-feedback variant of DP-SIGNSGD to improve accuracy. Experimental results on benchmark image datasets demonstrate the effectiveness of our proposed methods.