Purpose The purpose of this paper is to analyze the influence of curvature on the transport of low-density lipoprotein (LDL) through a curved artery and concentration boundary layer characteristics numerically. Design/methodology/approach By using a projection method based on the second-order central difference discretization, the authors solve the set of governing equations, which consists of Navier–Stokes, continuity and species transport. The effects of initial straight length, as well as the curvature and wall shear stress (WSS) on LDL transport in a curved artery are established in this paper. Findings The obtained numerical results imply that the LDL concentration boundary layer thickness decreases in the outer part of the curved artery and increases in the inner part for both with or without initial straight length. The effect of Reynolds number on the concentration distribution in a curved artery with initial straight length is more pronounced than that on a fully curved artery, although an opposite trend was seen for the curvature ratio. The maximum surface LDL concentration is related to the regions with minimum WSS in the inner part of the curved artery, which has more potential the formation of atherosclerosis. Originality/value The authors present a comprehensive concentration distribution of LDL in the concentration boundary layer of the curved artery. The authors also characterize and predict the influence of curvature on the formation and development of atherosclerosis within the arterial wall.