Liver segmentation is relevant for several clinical applications. Automatic liver segmentation using convolutional neural networks (CNNs) has been recently investigated. In this paper, we propose a new approach of combining a largest connected component (LCC) algorithm, as a post-processing step, with CNN approaches to improve liver segmentation accuracy. Specifically, in this study, the algorithm is combined with three well-known CNNs for liver segmentation: FCN-CRF, DRIU and V-net. We perform the experiment on a variety of liver CT images, ranging from non-contrast enhanced CT images to low-dose contrast enhanced CT images. The methods are evaluated using Dice score, Haudorff distance, mean surface distance, and false positive rate between the liver segmentation and the ground truth. The quantitative results demonstrate that the LCC algorithm statistically significantly improves results of the liver segmentation on non-contrast enhanced and low-dose images for all three CNNs. The combination with V-net shows the best performance in Dice score (higher than 90%), while the DRIU network achieves the smallest computation time (2 to 6 seconds) for a single segmentation on average. The source code of this study is publicly available at https://github.com/kennyha85/Liver-segmentation. Keywords: Liver segmentations, CNNs, Connected Components, Post processing Reference [1] K.A. McGlynn, J.L. Petrick, W.T. London, Global epidemiology of hepatocellular carcinoma: An emphasis on demographic and regional variability. Clinics in liver disease 19(2) (2015) 223-238. [2] M. Mohammadian, N. Mahdavifar, A. Mohammadian-Hafshejani, H. Salehiniya, Liver cancer in the world: epidemiology, incidence, mortality and risk factors, World Cancer Res J. 5(2) (2018) e1082. [3] T.T. Hong, N. Phuong Hoa, S.M. Walker, P.S. Hill, C. 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