Machinery health management becomes an essential issue in many sectors. The ultimate goal is to predict machinery degradation and accordingly plan maintenance actions. However, prediction becomes much harder if data is noisy. We propose a procedure for on-line prediction of the forthcoming machine state. This procedure is dedicated to the non-Gaussian (impulsive) health index (HI) data. It is based on a simplified degradation model with three machine states, i.e. healthy, warning and alarm, described in terms of a Hidden Markov Model (HMM). Using simulated trajectories we demonstrate that the α-stable HMM dedicated to time series with impulsive behaviour outperforms the classical Gaussian approach and can be an efficient alternative in such a case. In particular, the percentage errors of the predicted alarm state transition points decrease from 20%−45% to 1%−6%, if the α-stable HMM is used instead of the Gaussian one. We illustrate the proposed methodology for two datasets acquired during experiment on the VIBstand test rig and for a benchmark FEMTO dataset.