As large language models continue to scale up, the imperative for fault tolerance in distributed deep learning systems intensifies, becoming a focal area of AI infrastructure research. Checkpoint has emerged as the predominant fault tolerance strategy, with extensive studies dedicated to optimizing its efficiency. However, the advent of the sparse Mixture-of-Experts (MoE) model presents new challenges for traditional checkpoint techniques due to the substantial increase in model size, despite comparable computational demands to dense models. Breaking new ground in the realm of efficient fault tolerance for MoE model training, we introduce a novel Partial Experts Checkpoint (PEC) mechanism alongside a corresponding PEC fault-tolerant system. Our approach strategically checkpoints a selected subset of experts, thereby significantly reducing the checkpoint size for MoE models to a level comparable with that of dense models. The empirical analysis on our 8-expert GPT-MoE model demonstrates that the proposed PEC approach facilitates a substantial 54.2% decrease in the size of non-redundant checkpoint (no data-parallel duplication), without compromising the final model quality. Moreover, our PEC fault-tolerant system achieves a 76.9% reduction in checkpoint workload per data-parallel distributed rank, thereby correspondingly diminishing the checkpointing time and facilitating complete overlap with the training process.