It is very important for the normal operation of high-speed trains to assess the health status of the running gear system. In actual working conditions, many unknown interferences and random noises occur during the monitoring process, which cause difficulties in providing an accurate health status assessment of the running gear system. In this paper, a new data-driven model based on a slow feature analysis-support tensor machine (SFA-STM) is proposed to solve the problem of unknown interference and random noise by removing the slow feature with the fastest instantaneous change. First, the relationship between various statuses of the running gear system is analyzed carefully. To remove the random noise and unknown interferences in the running gear systems under complex working conditions and to extract more accurate data features, the SFA method is used to extract the slowest feature to reflect the general trend of system changes in data monitoring of running gear systems of high-speed trains. Second, slowness data were constructed in a tensor form to achieve an accurate health status assessment using the STM. Finally, actual monitoring data from a running gear system from a high-speed train was used as an example to verify the effectiveness and accuracy of the model, and it was compared with traditional models. The maximum sum of squared resist (SSR) value was reduced by 16 points, indicating that the SFA-STM method has the higher assessment accuracy.