Weight initialization is important for faster convergence and stability of deep neural networks training. In this paper, a robust initialization method is developed to address the training instability in long short-term memory (LSTM) networks. It is based on a normalized random initialization of the network weights that aims at preserving the variance of the network input and output in the same range. The method is applied to standard LSTMs for univariate time series regression and to LSTMs robust to missing values for multivariate disease progression modeling. The results show that in all cases, the proposed initialization method outperforms the state-of-the-art initialization techniques in terms of training convergence and generalization performance of the obtained solution.