It is difficult to develop accurate mathematical models to describe the range extender electric vehicles due to the nonlinear and complex coupling of the monitoring signal sources resulted from the massive moving parts and complex architecture in range extender and the limited storage space of the diagnostic device. In this study, we proposed the smooth iterative online support tensor machine algorithm, which is combined with support higher-order tensor machine and online stochastic gradient descent method, and applied it to the fault diagnosis of the range indicator. Four methods with different algorithms, support vector machine, smooth iterative online support vector machine, linear support higherorder tensor machine, and smooth iterative online support tensor machine algorithms, were adopted to diagnose and classify the fault samples of the range indicator by comparing the diagnostic accuracy and model learning time. It is found that the fault diagnosis method based on the smooth iterative online tensor machine showed a higher accuracy, shorter learning time, and less storage space. Based on the experimental results, it is feasible to apply smooth iterative online support tensor machine model to the fault diagnosis of electric vehicle extenders.