In recent years, the Mixture-of-Experts (MoE) technique has gained widespread popularity as a means to scale pre-trained models to exceptionally large sizes. Dynamic activation of experts allows for conditional computation, increasing the number of parameters of neural networks, which is critical for absorbing the vast amounts of knowledge available in many deep learning areas. However, despite the existing system and algorithm optimizations, there are significant challenges to be tackled when it comes to the inefficiencies of communication and memory consumption. In this paper, we present the design and implementation of MPMoE, a high-performance library that accelerates MoE training with adaptive and memory-efficient pipeline parallelism. Inspired by that the MoE training procedure can be divided into multiple independent sub-stages. We design a pipeline parallelism method for reducing communication latency by overlapping with computation operations. Further, we analyze the memory footprint breakdown of MoE training and identify that activations and temporary buffers are the primary contributors to the overall memory footprint. Toward memory efficiency, we propose memory reuse strategies to reduce memory requirements by eliminating memory redundancies. Finally, to optimize pipeline granularity and memory reuse strategies jointly, we propose a profile-based algorithm and a performance model to determine the configurations of MPMoE at runtime. We implement MPMoE upon PyTorch and evaluate it with common MoE models in two physical clusters, including 64 NVIDIA A100 GPU cards and 16 NVIDIA V100 GPU cards. Compared with the state-of-art approach, MPMoE achieves up to 2.3× speedup while reducing more than 30% memory footprint for training large models.