In any industrial system, accurate prediction of Remaining Useful Life (RUL) is important for Prognostics and Health Management (PHM), so as to detect breakdown of system well in advance and take proper measures. Different methods are available in the literature that have been proposed for prediction of RUL. Among these methods, the data driven method is accepted to be the most reliable by many researchers, due to the use of real time sensor based vibrational and/or pressure data. These data are acquired in time domain. Methods such as Recurrent Neural Networks (RNNs), Convolutional Neural Network (CNN), Hidden Markov Models (HMMs) are generally applied in this area. Nevertheless, all these methods have issues while dealing with dependencies in these data. In this context, Long Short-Term Memory (LSTM) neural network has been proposed to deal with these dependencies while predicting RUL of any system. The LSTM model has the advantage of retaining time domain information for a long duration of time. However, with the arrival of new data, the model needs to be updated. In this regard, a new online method based on LSTM network is proposed in this paper. The use of online technique offers us to retrain the model as new data arrives, which helps in improving the accuracy of the estimated RUL. To illustrate the application of the proposed online LSTM method, we have used the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) turbofan dataset. The results show an improved efficiency compared to the previously proposed methods for RUL estimation.