Glucose prediction is used in diabetes self-management as it allows to take suitable actions for proper glycemic regulation of the patient. The aim of this work is the short-term personalized glucose prediction in patients with Type 1 diabetes mellitus (T1DM). In this scope, we compared two different models, an autoregressive moving average (ARMA) model and a long short-term memory (LSTM) model for different prediction horizons. The comparison of two models was performed using the evaluation metrics of root mean square error (RMSE) and mean absolute error (MAE). The models were trained and tested in 29 real patients. The results shown that the LSTM model had better performance than ARMA with RMSE 3.13, 6.41 and 8.81 mg/dL and MAE 1.98, 5.06 and 6.47 mg/dL for 5-, 15- and 30-minutes prediction horizon.