Enabling private inference is crucial for many cloud inference services that are based on Transformer models. However, existing private inference solutions for Transformers can increase the inference latency by more than 60x or significantly compromise the quality of inference results. In this paper, we design the framework MPCFORMER using secure multi-party computation (MPC) and Knowledge Distillation (KD). It can be used in tandem with many specifically designed MPC-friendly approximations and trained Transformer models. MPCFORMER significantly speeds up Transformer model inference in MPC settings while achieving similar ML performance to the input model. We evaluate MPCFORMER with various settings in MPC. On the IMDb dataset, we achieve similar performance to BERTBASE, while being 5.3x faster. On the GLUE benchmark, we achieve 97% performance of BERTBASE with a 2.2x speedup. We show that MPCFORMER remains effective with different trained Transformer weights such as ROBERTABASE and larger models including BERTLarge. In particular, we achieve similar performance to BERTLARGE, while being 5.93x faster on the IMDb dataset.