In practice, the processes of degradation of inductive components and produced have long-range dependence characteristic, whereby the future degradation evolution is related to both current and previous states. Most known prediction models consider the degradation increments independent and the long-range dependence is not reflected. On the contrary, the heavy tail model can reveal the long-range dependence characteristic of the degradation processes.The contribution of this paper is to propose a new heavy tail degradation model, in which the fractional Lvy stable motion is used as a diffusion term to establish a degradation model with power rate drift. The difference iterative form of the fractional Lvy stable motion degradation model is, then, used to predict the remaining useful life. In the paper, this is applied to actual bearing degradation data and its prediction performance is analyzed. Variational mode decomposition is used to solve the problem that the degradation trend is not obvious for the vibration signals.