Mine hoists operate under high loads for extended periods of time. Early fault diagnosis and predictive maintenance of their key rotating components, the bearings, are important for the safe and efficient operation of hoisting systems. Existing diagnostic methods suffer from performance degradation in the hoist's complex working conditions. Therefore, an improved deep transfer learning diagnostic model was proposed, combining the fault response mechanism and signal time-frequency analysis techniques, and a cross-condition bearing fault diagnosis algorithm model CTJ-FDM was established. Firstly, a wavelet gram matrix group representation method was proposed. This constructed a matrix representation structure of the internal multi-scale features of the vibration signal's different frequency bands. Secondly, a multiple residual block parallel deep feature extraction network and a feature weight adaptive allocation mechanism were designed to realize the fusion extraction of deep features in different frequency bands. Finally, a more stable domain-adaptive deep transfer diagnostic network structure was created by combining multilayer maximum mean discrepancy loss and a domain adversarial mechanism to enhance the model's domain adaptation capability. Based on this, an online diagnosis and predictive maintenance system for the hoist's key components was developed. Following experimental validation, the cross-condition average accuracy of the model on two bearing test benches was 99.81% and 99.39% respectively, indicating improved cross-condition diagnostic capability.