Accurately identifying the pipeline leak size is crucial for risk assessment and timely rescue. In this study, a Convolutional Neural Network (CNN) based on Continuous Wavelet Transform (CWT) acoustic image transformation is proposed to identify small-sized leak in non-metallic pipes. Firstly, one-dimensional acoustic signals are filtered using the Piecewise Aggregate Approximation (PAA) algorithm to reduce noise and storage resource consumption. Then, the filtered signals are transformed into two-dimensional images by CWT to enrich signal feature information, serving as the input for the CNN. Further, a leak size recognition model based on CWT-CNN is established. The effectiveness of this model is verified using experimental data from a non-metallic pipeline leak test. A comparative analysis is conducted on diverse acoustic image transformation methods, including CWT, Gramian Angular Summation Field (GASF), and Relative Position Matrix (RPM). The results demonstrate the superiority of the CWT-CNN model in pipeline leak size recognition. Finally, the impact of the signal length in an acoustic image on recognition accuracy is also examined. The results demonstrate that when the signal length in an acoustic image is 0.75 s, the accuracy obtained by CWT-CNN can reach 95 %.