Missing observational data pose an unavoidable problem in the hydrological field. Deep learning technology has recently been developing rapidly, and has started to be applied in the hydrological field. Being one of the network architectures used in deep learning, Long Short-Term Memory (LSTM) has been applied largely in related research, such as flood forecasting and discharge prediction, and the performance of an LSTM model has been compared with other deep learning models. Although the tuning of hyperparameters, which influences the performance of an LSTM model, is necessary, no sufficient knowledge has been obtained. In this study, we tuned the hyperparameters of an LSTM model to investigate the influence on the model performance, and tried to obtain a more suitable hyperparameter combination for the imputation of missing discharge data of the Daihachiga River. A traditional method, linear regression with an accuracy of 0.903 in Nash–Sutcliffe Efficiency (NSE), was chosen as the comparison target of the accuracy. The results of most of the trainings that used the discharge data of both neighboring and estimation points had better accuracy than the regression. Imputation of 7 days of the missing period had a minimum value of 0.904 in NSE, and 1 day of the missing period had a lower quartile of 0.922 in NSE. Dropout value indicated a negative correlation with the accuracy. Setting dropout as 0 had the best accuracy, 0.917 in the lower quartile of NSE. When the missing period was 1 day and the number of hidden layers were more than 100, all the compared results had an accuracy of 0.907–0.959 in NSE. Consequently, the case, which used discharge data with backtracked time considering the missing period of 1 day and 7 days and discharge data of adjacent points as input data, indicated better accuracy than other input data combinations. Moreover, the following information is obtained for this LSTM model: 100 hidden layers are better, and dropout and recurrent dropout levels equaling 0 are also better. The obtained optimal combination of hyperparameters exceeded the accuracy of the traditional method of regression analysis.