Since the outbreak of the Coronavirus Disease 2019 (COVID-19), the spread of the epidemic has been a major international public health issue. Hence, various forecasting models have been used to predict the infectious spread of the disease. In general, forecasting problems often involve prediction accuracy decreasing as the horizon increases. Thus, to extend the forecasting horizon without decreasing performance or prediction, this study developed a Dual Long Short-Term Memory (LSTM) with Genetic Algorithms (DULSTMGA) model. The model employed predicted values generated by LSTM models in short-forecasting horizons as inputs for the long-term prediction of LSTM in a rolling manner. Genetic algorithms were applied to determine the parameters of LSTM models, allowing long-term forecasting accuracy to increase as long as short-term forecasting was accurate. In addition, the compartment model was utilized to simulate the state of COVID-19 and generate numbers of infectious cases. Infectious cases in three countries were employed to examine the feasibility and performance of the proposed DULSTMGA model. Numerical results indicated that the DULSTMGA model could obtain satisfactory forecasting accuracy and was superior to many previous studies in terms of the mean absolute percentage error. Therefore, the designed DULSTMGA model is a feasible and promising alternative for forecasting the number of infectious COVID-19 cases.