COVID-19 has been one of the most severe diseases, causing a harsh pandemic all over the world, since December 2019. The aim of this study is to evaluate the value of Long Short-Term Memory (LSTM) Networks in forecasting the total number of COVID-19 cases in Turkey. The COVID-19 data for 30 days, between March 24 and April 23, 2020, are used to estimate the next fifteen days. The mean absolute error of the LSTM Network for 15 days estimation is 1,69$\pm$1.35%. Whereas, for the same data, the error of the Box-Jenkins method is 3.24$\pm$1.56%, Prophet method is 6.88$\pm$4.96% and Holt-Winters Additive method with Damped Trend is 0.47$\pm$0.28%. Additionally, when the number of deaths data is also provided with the number of total cases to the input of LSTM Network, the mean error reduces to 0.99$\pm$0.51%. Consequently, addition of the number of deaths data to the input, results a lower error in forecasting, compared to using only the number of total cases as the input. However, Holt-Winters Additive method with Damped Trend gives superior results to LSTM Networks in forecasting the total number of COVID-19 cases.