We introduce a new method for normalization of data acquired by liquid chromatography coupled with mass spectrometry (LC-MS) in label-free differential expression analysis. Normalization of LC-MS data is desired prior to subsequent statistical analysis to adjust variabilities in ion intensities that are not caused by biological differences but experimental bias. There are different sources of bias including variabilities during sample collection and sample storage, poor experimental design, noise, etc. In addition, instrument variability in experiments involving a large number of LC-MS runs leads to a significant drift in intensity measurements. Although various methods have been proposed for normalization of LC-MS data, there is no universally applicable approach. In this paper, we propose a Bayesian normalization model (BNM) that utilizes scan-level information from LC-MS data. Specifically, the proposed method uses peak shapes to model the scan-level data acquired from extracted ion chromatograms (EIC) with parameters considered as a linear mixed effects model. We extended the model into BNM with drift (BNMD) to compensate for the variability in intensity measurements due to long LC-MS runs. We evaluated the performance of our method using synthetic and experimental data. In comparison with several existing methods, the proposed BNM and BNMD yielded significant improvement.