In view of the defect of previous signal processing methods, a new non-stationary signal analysis method, namely, the sparse bandwidth mode decomposition (SBMD) was proposed. The essence of the method is that the signal decomposition is converted into a constrained variational problem, and the signal is decomposed into a set of IMFs by SBMD. In addition, the vibration signals of roller bearings with variable speed usually contain more comprehensive status information, so, the SBMD combined with the order tracking and envelope spectrum analysis is suitable for applying in the fault diagnosis of roller bearings under the working condition of variable speed. The experimental results validate that the approach can handle the variable speed roller bearing fault diagnosis accurately and effectively. © 2017, Editorial Office of Journal of Vibration and Shock. All right reserved.