Wheelset bearing is a typical vulnerable structural component in high-speed trains and heavy haul vehicles. In addition to the typical nonlinear and nonstationary characteristics, the vibration signal of wheelset bearing also contains track subgrade vibration and transmission path coupling interference components. To solve this problem, this paper proposes a new feature extraction method for wheelset bearing faults. This method constructs the Teager energy spectrum correlation kurtosis, which is purposely sensitive to periodic fault impulse components, as the objective function. The Q-factor and redundancy of tunable Q-factor wavelet transform are selected by using the parameter convex optimization method, which makes the signal decomposition have better sparsity, so as to extract fault information accurately. Simulated analysis, experimental signal analysis of QPZZ-II test-bed, and experimental signal analysis of wheelset bearing test-bed show that the proposed method can suppress the influence of nonperiodic transient impulse components, harmonic components, and noise components in the signal and accurately extract the periodic impact characteristics of bearings.