Vital signs including heart rate, respiratory rate, body temperature and blood pressure, are critical in the clinical decision making process. Effective early prediction of vital signs help to alert medical practitioner ahead of time and may prevent adverse health outcomes. In this paper, we suggest a new approach called generative boosting, in order to effectively perform early prediction of vital signs. Generative boosting consists of a generative model, to generate synthetic data for next few time steps, and several predictive models, to directly make long-range predictions based on observed and generated data. We explore generative boosting via long short-term memory (LSTM) for both the predictive and generative models, leading to a scheme called generative LSTM (GLSTM). Our experiments indicate that GLSTM outperforms a diverse range of strong benchmark models, with and without generative boosting. Finally, we use a mutual information based clustering algorithm to select a more representative dataset to train the generative model of GLSTM. This significantly improves the long-range predictive performance of high variation vital signs such as heart rate and systolic blood pressure.