In the process of extracting the fault characteristic signal of wheelset bearing using graph Fourier transform （GFT） method， the noise components contained in the signal will be extracted together， which will affect the fault diagnosis. To solve this problem， a fault diagnosis method of wheelset bearing based on sparse representation and spectrum theory is proposed. Firstly， using sparse representation method to restructure wheelset bearing vibration signal with local damage. Then， using the GFT method to process these signals， the impulse components contained in the signal are concentrated in the higher order region of the GFT graph spectrum. Through analysis those impulse components， bearing fault can be detected. The validity of the proposed method is proved by the results which get using this method to process the simulation data and the bench test data.