When a subway train runs on a small radius curve, it causes serious side wear of the outer rail, and a large number of the outer rails of the curve are replaced frequently due to excessive side wear. This paper proposes three prediction models based on the response surface methodology (RSM), support vector machine (SVM), and the relative vector machine (RVM) to estimate the remaining useful life (RUL) of a metro outer rail at a small radius curve determined by rail side wear. In these proposed models, the directly measurable parameters, including various track geometries, axle loads, and primary suspension stiffnesses related to vehicle types, are taken into account. These parameters are proposed from the side wear mechanism and subjected to the method of global sensitivity analysis to rank them in order of importance. The rail side wear for various scenarios is calculated through a numerical simulation model of the vehicle-unballasted track and Specht friction wear. Furthermore, with the help of simulation experiments and field cases, the prediction performances of three different prediction models are analyzed in detail. The comparison indicates that the predictive model based on RVM is superior in the prediction of RUL based on rail wear. The findings presented in this paper can provide certain reference values for infrastructure managers (IMs).