The roller bearing fault vibration signals in the rotating speed-varying condition have characteristics that include multi-component modulation. Fault characteristic frequency is modulated by rotating frequency, which makes fault characteristics extraction difficult. In light of this, a new roller bearing fault diagnosis method is proposed that combines local mean decomposition (LMD) with order tracking analysis. First, the roller bearing fault vibration signals in the time domain are transformed into an angle domain using order tracking sampling. Then, the angle domain signals are decomposed by LMD to obtain a set of product functions (PFs). Finally, the instantaneous envelope of each PF is analyzed using the frequency spectrum to determine the roller bearing fault position and type. The results from the experimental fault vibration signals of the roller bearing demonstrate that the proposed method can be effectively applied to the roller bearing fault diagnosis in the rotating speed-varying condition.