The increasing frequency of devastating floods from heavy rainfall associated with climate change has made river stage prediction more important. For steep, forest-covered mountainous watersheds, deep learning models may improve prediction of river stages from rainfall. Here we use the framework of multilayer perceptron (MLP) neural networks to develop such a river stage model. The MLP is constructed for the Shimanto river, which lies in southwestern Japan under a mild, rain-heavy climate. Our input for stage estimation, as well as prediction, is long-term rainfall time series. With a one-year time series of rainfall, the model estimates the stage with 50 cm RMSE for about 10 m of stage peaks as well as accurately simulate stage-time fluctuations. Furthermore, the forecast model can predict the stage without rainfall forecasts up to three hours ahead. To estimate the base flow stages as well as flood peaks with high precision we find the rainfall time series should be at least one year. This indicates that the use of a long rainfall time series enables one to model the contributions of ground water and evaporation. Given that the delay between the arrival time of rainfall at a rain-gauge to the outlet change is well simulated, the physical concepts of runoff appear to be soundly embedded in the MLP.