The unprecedented impact of the COVID-19 pandemic has revealed that forecasting capability is critically needed in making strategic decisions and formulating reasonable countermeasures. This study aimed to assess the predictive accuracy in forecasting the numbers of COVID-19 cases using Thailand’s national COVID-19 surveillance database from January 2020– June 2021 based on three analytical models: a susceptible-exposed-infectious-recovery compartmental model, an auto-regressive integrated moving average model, and a long short-term memory (LSTM) network model. All forecasting methods had model parameters adjusted weekly according to the most recent situation and predictive accuracy measures, including the mean absolute percent error (MAPE). We found that the MAPE values ranged from 19.65%–22.54%, 28.95%–32.35%, 47.78%–53.55%, and 75.03–84.91% for forecasting one, two, four, and eight weeks ahead, respectively. Among the three models, the LSTM model had slightly higher accuracy than the other two models within the same forecasting range. These prediction models can be used for short-range forecasts in other similar settings while long-range forecasting requires monitoring and updating periodically.