Road pavements need to be efficiently maintained under budget constraints. A pavement management system supports a road administrator's decision making based on the prediction of pavement deterioration. However, the prediction of pavement deterioration is complicated and uncertain because there are many unobservable variables, and the highly accurate prediction of deterioration is difficult. For pavement administrators to use such predictions in decision making, it is necessary to quantify the reliability of prediction. This paper proposes a prediction interval estimation method by applying the bootstrap method with a reduced computational cost to the deterioration prediction model using a neural network. The proposed method is applied to the rutting depth prediction in the inspection history of road pavement surface, and the estimation accuracy of the prediction interval is verified. In the prediction model, because the inspection history is time-series data, a recurrent neural network model that extends neural networks to time series prediction is used. Verification shows that not only is the computational cost reduced but also the accuracy of the prediction interval is higher than that of the conventional method.