This study proposes a new deep recurrent neural network approach, Neural Runoff Model (NRM), which has been applied on 125 USGS streamflow gages in the State of Iowa for predicting the next 120 h due to the difficult nature of accurate streamflow forecasting. The proposed model outperforms the streamflow persistence, ridge regression and random forest regression on majority of the gages. The model has also shown strong predictive power and can be used for long-term streamflow predictions.