Prompting has recently been shown as a promising approach for applying pre-trained language models to perform downstream tasks. We present Multi-Stage Prompting (MSP), a simple and automatic approach for leveraging pre-trained language models to translation tasks. To better mitigate the discrepancy between pre-training and translation, MSP divides the translation process via pre-trained language models into multiple separate stages: the encoding stage, the re-encoding stage, and the decoding stage. During each stage, we independently apply different continuous prompts for allowing pre-trained language models better shift to translation tasks. We conduct extensive experiments on three translation tasks. Experiments show that our method can significantly improve the translation performance of pre-trained language models.