The damage caused by floods is increasing worldwide, and if floods can be predicted, the economic and human losses from floods can be reduced. A key parameter of flooding is water level data, and this paper proposes a water level prediction model using long short-term memory (LSTM) and a gated recurrent unit (GRU). As variables used as input data, meteorological data, including upstream and downstream water level, temperature, humidity, and precipitation, were used. The best results were obtained when the LSTM–GRU-based model and the Automated Synoptic Observing System (ASOS) meteorological data were included in the input data when experiments were performed with various model structures and different input data formats. As a result of the experiment, the mean squared error (MSE) value was 3.92, the Nash–Sutcliffe coefficient of efficiency (NSE) value was 0.942, and the mean absolute error (MAE) value was 2.22, the highest result in all cases. In addition, the test data included the historical maximum water level of 3552.38 cm in the study area, and the maximum water level error was also recorded as 55.49, the lowest result. Through this paper, it was possible to confirm the performance difference according to the composition of the input data and the time series prediction model. In a future study, we plan to implement a flood risk management system that can use the predicted water level to determine the risk of flooding, and evacuate in advance.