Developing an accurate and reliable multi-step ahead prediction model is a key problem in many Prognostics and Health Management (PHM) applications. Inevitably, the further one attempts to predict into the future, the harder it is to achieve an accurate and stable prediction due to increasing uncertainty and error accumulation. In this paper, we address this problem by proposing a prediction model based on Long Short-Term Memory (LSTM), a deep neural network developed for dealing with the longterm dependencies in time-series data. Our proposed prediction model also tackles two additional issues. Firstly, the hyperparameters of the proposed model are automatically tuned by a Bayesian optimization algorithm, called Tree-structured Parzen Estimator (TPE). Secondly, the proposed model allows assessing the uncertainty on the prediction. To validate the performance of the proposed model, a case study considering steam generator data acquired from different French nuclear power plants (NPPs) is carried out. Alternative prediction models are also considered for comparison purposes.