Deep learning using large models have achieved great success in a wide range of domains. However, training these models on billions of parameters is very challenging in terms of the training speed, memory cost, and communication efficiency, especially under the privacy-preserving regime with differential privacy (DP). On the one hand, DP optimization has comparable efficiency to the standard non-private optimization on a single GPU, but on multiple GPUs, existing DP distributed learning (such as pipeline parallel) has suffered from significantly worse efficiency. On the other hand, the Zero Redundancy Optimizer (ZeRO) is a state-of-the-art solution to the standard distributed learning, exhibiting excellent training efficiency on large models, but to work compatibly with DP is technically complicated. In this work, we develop a new systematic solution, DP-ZeRO, (I) to scale up the trainable DP model size, e.g. to GPT-100B, (II) to obtain the same computation and communication efficiency as the standard ZeRO, and (III) to enable mixed-precision DP training. Our DP-ZeRO, like the standard ZeRO, has the potential to train models with arbitrary size and is evaluated on the world's largest DP models in terms of the number of trainable parameters.