We introduce EdgeFormer – a parameter-efficient Transformer for on-device seq2seq generation under the strict computation and memory constraints. Compared with the previous parameter-efficient Transformers, EdgeFormer applies two novel principles for cost-effective parameterization, allowing it to perform better given the same parameter budget; moreover, EdgeFormer is further enhanced by layer adaptation innovation that is proposed for improving the network with shared layers.Extensive experiments show EdgeFormer can effectively outperform previous parameter-efficient Transformer baselines and achieve competitive results under both the computation and memory constraints. Given the promising results, we release EdgeLM – the pretrained version of EdgeFormer, which is the first publicly available pretrained on-device seq2seq model that can be easily fine-tuned for seq2seq tasks with strong results, facilitating on-device seq2seq generation in practice.