This study proposes a novel rolling bearing fault diagnosis technique based on a synchrosqueezing wavelet transform (SWT) and a transfer residual convolutional neural network (TRCNN) designed to address the difficulties of feature extraction caused by the non-stationarity of fault signals, as well as the issue of low fault diagnosis accuracy resulting from small sample quantities. This approach transforms the one-dimensional vibration signal into time–frequency diagrams using an SWT based on complex Morlet wavelet basis functions, which redistributes (squeezes) the values of the wavelet coefficients at different localized points in a time–frequency plane to the estimated instantaneous frequencies. This allows the energy to be more fully concentrated in actual corresponding frequency components. This strategy improves both the time–frequency aggregation and the resolution, which better reflects the eigenvalues of non-stationary signals. In this process, transfer learning and a residual structure are used in the training of a convolutional neural network. The resulting time–frequency diagrams, acquired using the steps discussed above, are then input to the TRCNN for diagnosis. A series of validation experiments confirmed that applying the TRCNN structure made it possible to achieve high diagnostic accuracy, even when training the network with only a small number of fault samples, as all 12 fault types from the test dataset were diagnosed correctly. Further simulation experiments demonstrated that our proposed method improved fault diagnosis accuracy compared to that of conventional techniques (with increases of 1.74% over RCNN, 1.28% over TCNN, 1.62% over STFT, 1.73% over WT, 2.83% over PWVD, and 1.39% over STFA-PD). In addition, diagnostic accuracy reached 100% during the application of three-time transfer learning, validating the effectiveness of the proposed method for rolling bearing fault diagnosis.