In the context of time-series forecasting, we propose a LSTM-based recurrent neural network architecture and loss function that enhance the stability of the predictions. In particular, the loss function penalizes the model, not only on the prediction error (mean-squared error), but also on the predicted variation error. We apply this idea to the prediction of future glucose values in diabetes, which is a delicate task as unstable predictions can leave the patient in doubt and make him/her take the wrong action, threatening his/her life. The study is conducted on type 1 and type 2 diabetic people, with a focus on predictions made 30-min ahead of time. First, we confirm the superiority, in the context of glucose prediction, of the LSTM model by comparing it to other state-of-the-art models (Extreme Learning Machine, Gaussian Process regressor, Support Vector Regressor). Then, we show the importance of making stable predictions by smoothing the predictions made by the models, resulting in an overall improvement of the clinical acceptability of the models at the cost in a slight loss in prediction accuracy. Finally, we show that the proposed approach, outperforms all baseline results. More precisely, it trades a loss of 4.3% in the prediction accuracy for an improvement of the clinical acceptability of 27.1%. When compared to the moving average post-processing method, we show that the trade-off is more efficient with our approach.