Abstract: A new method for monitoring the running state of the high-speed railway's gearbox based on the extension theory was proposed. By extracting the suitable characteristic parameters, the matter-element models of the gearbox in vibration directions during its normal operating status were established. A new evolutionary algorithm, the particle swarm optimization (PSO) algorithm was used to get the characteristic parameters' classical domains. On the basis of the classical domains' optimization results and the dependent function, the running status monitoring system of the gearbox was designed based on the Matlab GUI. This system can qualitatively and quantitatively estimate the current running condition of the gearbox in vibration directions. The results of the monitoring system show a good consistency with the gearbox's actual running state, and verify the accuracy of the monitoring method based on the extension theory.