A novel non-stationary signal method differential operator based LCD(DOLCD) was proposed for improving the LCD method, of which, when the target signal contained components with frequencies close to each other, the decomposition ability was decreased, mode mixing phenomenon would easily occur and the physical meaning of intrinsic scale components decomposed were lost. A differential operator was used to differentiate the target signal in time domain, then the differentiated target signal was decomposed with DOLCD, then in the certain frequency ratio, the decomposition ability was enhanced, and the mode mixing was inhibited. The paper firstly studied the theory of DOLCD, then simulation experiments were used to compare the decomposition ability of DOLCD with LCD. The results indicate that DOLCD is more efficient in improving the decomposition ability, and inhibiting the mode mixing than LCD. Finally, the proposed method was applied to diagnose the rotor with misalignment faults successfully which indicated the effectiveness of DOLCD.