Aiming at the extraction problem for weak fault eigenfrequency submerged in strong colored noises, a novel method based on higher-order cumulant and multitaper spectral was introduced. The higher-order cumulant of the signal was constructed firstly, and then bispectrum could be obtained by using multitaper spectral analysis for the higher-order cumulant. The primary fault feature could be extracted from the diagonal slice of bispectrum. Owing to the nonlinear phase coupling relation between the fault eigenfrequencies and fundamental frequency, a quadratic phase coupling analysis was implemented based on the multitaper bispectrum. According to the quadratic phase coupling analysis, those weak fault eigenfrequencies were easily identified. Finally, an experiment was arranged in laboratory, and the bear faults were put into the motor. By using the method proposed, it is validated that multitaper bispectrum is effective for identifying weak fault eigenfrequency in motor.