In this paper, we propose an additionsubtraction twin-gated recurrent network (ATR) to simplify neural machine translation. The recurrent units of ATR are heavily simplified to have the smallest number of weight matrices among units of all existing gated RNNs. With the simple addition and subtraction operation, we introduce a twin-gated mechanism to build input and forget gates which are highly correlated. Despite this simplification, the essential non-linearities and capability of modeling long-distance dependencies are preserved. Additionally, the proposed ATR is more transparent than LSTM/GRU due to the simplification. Forward self-attention can be easily established in ATR, which makes the proposed network interpretable. Experiments on WMT14 translation tasks demonstrate that ATR-based neural machine translation can yield competitive performance on English-German and English-French language pairs in terms of both translation quality and speed. Further experiments on NIST Chinese-English translation, natural language inference and Chinese word segmentation verify the generality and applicability of ATR on different natural language processing tasks.