Rolling bearings are key components that support the rotation of motor shafts, operating with a quite high failure rate among all the motor components. Early bearing fault diagnosis has great significance to the operation security of motors. The main contribution of this paper is to illustrate Gaussian white noise in bearing vibration signals seriously masks the weak fault characteristics in the diagnosis based on the Teager–Kaiser energy operator envelope, and to propose improved TKEO taking both accuracy and calculation speed into account. Improved TKEO can attenuate noise in consideration of computational efficiency while preserving information about the possible fault. The proposed method can be characterized as follows: a series of band-pass filters were set up to extract several component signals from the original vibration signals; then a denoised target signal including fault information was reconstructed by weighted summation of these component signals; finally, the Fourier spectrum of TKEO energy of the resulting target signal was used for bearing fault diagnosis. The improved TKEO was applied to a vibration signal dataset of run-to-failure rolling bearings and compared with two advanced diagnosis methods. The experimental results verify the effectiveness and superiority of the proposed method in early bearing fault detection.