Abstract The degradation process of lithium-ion batteries has memory, i.e. it has long-range dependence (LRD). In this paper, an iterative model of the generalized Cauchy (GC) process with LRD characteristics is proposed for the remaining useful life (RUL) prediction of lithium-ion batteries. The GC process uses two independent parameters, fractal dimension and Hurst exponent, to measure the LRD of the degradation process. The diffusion term of the GC iterative model is replaced by the increment of the GC time sequences, constructed via the autocorrelation function (ACF) to describe uncertainty and the LRD characteristics of the lithium-ion batteries capacity degradation. Linear and nonlinear drift terms are used to explain the degradation trend of the lithium-ion batteries capacity. A comparison is made with fractional Brownian motion (FBM) and long-short-term memory (LSTM) network models to show how the GC iterative model has the best performance in RUL prediction of lithium-ion batteries.