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• A feature-compressed multi-task learning U-Net with CBAM (MTL-UNET-CBAM) for shallow-water source localization with the presence of internal waves is constructed. • CBAM improves range localization performance of MTL-UNET, but has no significant improvement on depth estimation. • MTL-UNET-CBAM has higher localization robustness and computation speed then CMFP. • Applying DTL to MTL-UNET-CBAM significantly improve the localization performance of MTL-UNET-CBAM on both range and depth estimation. The spatiotemporal variation of sound speed profile caused by internal waves usually causes the mismatch in the Matched-Field Processing (MFP) source localization. A feature-compressed multi-task learning U-Net with Convolutional Block Attention Module (MTL-UNET-CBAM) is proposed to estimate the range and depth of underwater sources in the South China Sea environment with the presence of internal waves. To handle the mismatch caused by internal waves, the temperature sensor chain data are used to reconstruct the two-dimensional sound speed profiles (2D-SSPs) based on the 2D advection model. Then, 2D-SSPs are used to generate the training set with the parabolic equation method. Sensitivity analysis is investigated to examine the effects of sound speed profile mismatch on the source localization performance. The simulation result shows the higher robustness of MTL-UNET-CBAM to the sound speed profile mismatch compared with the conventional Matched-Field Processing (CMFP) method. Experiment data in the South China Sea also used to validate the source localization performance of MTL-UNET-CBAM. [ABSTRACT FROM AUTHOR]