The segmentation of the liver is a difficult process due to the changes in shape, border, and density that occur in each section in computed tomography (CT) images. In this study, the Adding Inception Module-Unet (AIM-Unet) model, which is a hybridization of convolutional neural networks-based Unet and Inception models, is proposed for computer-assisted automatic segmentation of the liver and liver tumors from CT scans of the abdomen. Experimental studies were carried out on four different liver CT image datasets, one of which was prepared for this study and three of which were open (CHAOS, LIST, and 3DIRCADb). The results obtained using the proposed method and the segmentation results marked by the specialist were compared with the Dice similarity coefficient (DSC), Jaccard similarity coefficient (JSC), and accuracy (ACC) measurement parameters. In this study, we obtained the best DSC, JSC, and ACC liver segmentation performance metrics on the CHAOS dataset as 97.86%, 96.10%, and 99.75%, respectively, of the AIM-Unet model we propose, which is trained separately on three datasets (LiST, CHAOS, and our dataset) containing liver images. Additionally, 75.6% and 65.5% of the DSC tumor segmentation metrics were calculated on the proposed model LiST and 3DIRCADb datasets, respectively. In addition, the segmentation success results on the datasets with the AIM-Unet model were compared with the previous studies. With these results, it has been seen that the method proposed in this study can be used as an auxiliary tool in the decision-making processes of physicians for liver segmentation and detection of liver tumors. This study is useful for medical images, and the developed model can be easily developed for applications in different organs and other medical fields.