The evaluation of well integrity in double-casing wells is critical for ensuring well stability, preventing oil and gas leaks, avoiding pollution, and ensuring safety throughout well development and production. However, the current predominant method of assessing cementing quality primarily focuses on single-casing wells, with limited work conducted on double-casing wells. This study introduces a novel approach for evaluating the cementing quality using the Inception module of convolutional neural networks. First, the finite-difference method is employed to generate borehole sonic data corresponding to a variety of model configurations, which are used to train a neural network that learns spatial features from the borehole sonic data to reconstruct the slowness model. By adjusting the network architecture and parameters, it is discovered that a neural network with two blocks and 4096 nodes in the fully connected layer demonstrated the best imaging results and exhibited strong anti-noise capabilities. The proposed method is validated using practical wellbore size models, demonstrating excellent results and offering a more effective means of evaluating wellbore integrity in double-casing wells. In addition, dipole acoustic logging data are used to conduct slowness model imaging of the compressional (P-) wave and shear (S-) wave in double-casing wells to verify the feasibility of cementing quality evaluation. The developed method contributes to more accurate evaluations of wellbore integrity for the oil and gas industry, leading to improved safety and environmental outcomes.