The original impulse components in rolling bearing incipient fault signals are difficult to be extracted since they are always covered by strong noise. Aiming at this problem, a new fault diagnosis method for rolling bearing incipient faults based on the multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) and Teager energy operator was proposed. Firstly, an original fault signal was filtered by MOMEDA then the Teager energy operator was used to enhance the deconvolution signal. Finally, in order to find the fault frequency, the envelope analysis was employed to deal with the processed signal. The fault location of the rolling bearing was extracted by contrasting the major frequency with the fault frequency of the rolling bearing, therefore, the fault type of the rolling bearing was confirmed. The analysis results of simulated signals and measured signals show that the proposed method is able to extract fault impulse signals and it is kind to practicability.