Rolling bearing plays an important role in rotary machines and industrial processes. Effective fault diagnosis technology for rolling bearing directly affects the life and operator safety of the devices. In this paper, a fault diagnosis method based on tunable-Q wavelet transform (TQWT) and convolutional neural network (CNN) is proposed to reduce the influence of noise on bearing vibration signal and the dependence on the experience of traditional diagnosis methods. TQWT is used to decompose and denoise the vibration signal, while the CNN is adopted to extract fault features and carry out fault classification. Seven motor operating conditions—normal, drive end rolling ball failure (DE-B), drive end inner raceway failure (DE-IR), drive end outer raceway failure (DE-OR), fan end rolling ball failure (FE-B), fan end inner raceway fault (FE-IR) and fan end outer raceway fault (FE-OR)—are used to evaluate the proposed approach. The experimental results indicate that the fault diagnosis accuracy of the proposed method reaches 99.8%.