In the multi-organ segmentation task of medical images, there are some challenging issues such as the complex background, blurred boundaries between organs, and the larger scale difference in volume. Due to the local receptive fields of conventional convolution operations, it is difficult to obtain desirable results by directly using them for multi-organ segmentation. While Transformer-based models have global information, there is a significant dependency on hardware because of the high computational demands. Meanwhile, the depthwise convolution with large kernel can capture global information and have less computational requirements. Therefore, to leverage the large receptive field and reduce model complexity, we propose a novel CNN-based approach, namely adjacent-scale fusion U-Net with large kernel (ASF-LKUNet) for multi-organ segmentation. We utilize a u-shaped encoder–decoder as the base architecture of ASF-LKUNet. In the encoder path, we design the large kernel residual block, which combines the large and small kernels and can simultaneously capture the global and local features. Furthermore, for the first time, we propose an adjacent-scale fusion and large kernel GRN channel attention that incorporates the low-level details with the high-level semantics by the adjacent-scale feature and then adaptively focuses on the more global and meaningful channel information. Extensive experiments and interpretability analysis are made on the Synapse multi-organ dataset (Synapse) and the ACDC cardiac multi-structure dataset (ACDC). Our proposed ASF-LKUNet achieves 88.41% and 89.45% DSC scores on the Synapse and ACDC datasets, respectively, with 17.96M parameters and 29.14 GFLOPs. These results show that our method achieves superior performance with favorable lower complexity against ten competing approaches.ASF-LKUNet is superior to various competing methods and has less model complexity. Code and the trained models have been released on GitHub.