Liver segmentation and recognition from computed tomography (CT) images is a warm topic in image processing which is helpful for doctors and practitioners. Currently, many deep learning methods are used for liver segmentation that takes a long time to train the model which makes this task challenging and limited to larger hardware resources. In this research, we proposed a very lightweight convolutional neural network (CNN) to extract the liver region from CT scan images. The suggested CNN algorithm consists of 3 convolutional and 2 fully connected layers, where softmax is used to discriminate the liver from background. Random Gaussian distribution is used for weight initialization which achieved a distance-preserving-embedding of the information. The proposed network is known as Ga-CNN (Gaussian-weight initialization of CNN). General experiments are performed on three benchmark datasets including MICCAI SLiver'07, 3Dircadb01, and LiTS17. Experimental results show that the proposed method performed well on each benchmark dataset.