Large-scale deep learning models contribute to significant performance improvements on varieties of downstream tasks. Current data and model parallelism approaches utilize model replication and partition techniques to support the distributed training of ultra-large models. However, directly deploying these systems often leads to sub-optimal training efficiency due to the complex model architectures and the strict device memory constraints. In this paper, we propose Optimal Sharded Data Parallel (OSDP), an automated parallel training system that combines the advantages from both data and model parallelism. Given the model description and the device information, OSDP makes trade-offs between the memory consumption and the hardware utilization, thus automatically generates the distributed computation graph and maximizes the overall system throughput. In addition, OSDP introduces operator splitting to further alleviate peak memory footprints during training with negligible overheads, which enables the trainability of larger models as well as the higher throughput. Extensive experimental results of OSDP on multiple different kinds of large-scale models demonstrate that the proposed strategy outperforms the state-of-the-art in multiple regards.