This paper presents Self-correcting Encoding (Secoco), a framework that effectively deals with noisy input for robust neural machine translation by introducing self-correcting predictors. Different from previous robust approaches, Secoco enables NMT to explicitly correct noisy inputs and delete specific errors simultaneously with the translation decoding process. Secoco is able to achieve significant improvements over strong baselines on two real-world test sets and a benchmark WMT dataset with good interpretability. We will make our code and dataset publicly available soon.