In the present study, we investigate blood flow and mass transfer of the low-density lipoprotein (LDL) in a simplified axisymmetric geometry with a mathematically well-defined narrowing (stenosis), which mimics a diseased human coronary artery. The interior of the arterial wall is represented as a porous media containing multi-layered structures of different thickness. This multi-layered structure includes anatomically realistic sublayers: endothelium, intima, internal elastic layer (IEL), media and adventitia. The coupling between the blood flow and mass transfer of LDL in the lumen (interior of artery) and arterial wall is established through a multipore model at the lumen/endothelium interface. This multipore model takes into consideration three different contributions for transport of LDL: normal and leaky junctions of endothelial cells, as well as their vesicular pathway. A comprehensive mathematical model, which is based on solving the set of PDEs for conservation of mass, momentum, and concentration, is completed by introducing the wall shear-stress (WSS) dependent transport properties of the arterial wall. Several variants of the model are evaluated, including the constant and wall shear-stress dependent transport properties of the endothelium, as well as different representation of the arterial wall internal structure. The response of the model on changing the transmural pressure (to simulate hypertension effects) and geometrical shapes of the stenosis (to mimic the various stages of atherosclerosis development) is also presented. It is shown that the present model can predict the levels of LDL inside the arterial wall in good agreement with experimental studies in pressurized rabbit aorta under similar conditions. The model is recommended for future simulations of LDL accumulation in the patient-specific cardiovascular system conditions.