Given a large Transformer model, how can we obtain a small and computationally efficient model which maintains the performance of the original model? Transformer has shown significant performance improvements for many NLP tasks in recent years. However, their large size, expensive computational cost, and long inference time make it challenging to deploy them to resource-constrained devices. Existing Transformer compression methods mainly focus on reducing the size of the encoder ignoring the fact that the decoder takes the major portion of the long inference time. In this paper, we propose PET (Parameter-Efficient knowledge distillation onTransformer), an efficient Transformer compression method that reduces the size of both the encoder and decoder. In PET, we identify and exploit pairs of parameter groups for efficient weight sharing, and employ a warm-up process using a simplified task to increase the gain through Knowledge Distillation. Extensive experiments on five real-world datasets show that PET outperforms existing methods in machine translation tasks. Specifically, on the IWSLT’14 EN→DE task, PET reduces the memory usage by 81.20% and accelerates the inference speed by 45.15% compared to the uncompressed model, with a minor decrease in BLEU score of 0.27.