In this work, a finite-difference-based axisymmetric off-lattice Boltzmann solver is developed to simulate blood flow through pathological arteries. The proposed solver handles arterial geometries using a body-fitted curvilinear mesh. The axisymmetric nature of the flow and the non-Newtonian behavior of blood are incorporated using external source terms. The solver is verified for spatially developing pulsatile inflow through an abdominal aortic aneurysm using reference data from literature. Thereafter, the effects of amplitude and frequency of an irregular-shaped stenosed artery are systematically studied. The results are analyzed using the instantaneous vorticity contours, streamlines, cycle-averaged and phase-averaged profiles of wall shear stress (WSS), and oscillatory shear index. Further, the correlation between the luminal surface concentration (LSC) of low-density lipoproteins and the WSS is studied to predict potential disease initiation and progression locations. It is noted that an increase in the amplitude of irregularity of the stenosis increases the magnitudes of maxima and minima of WSS profiles without altering their locations. On the other hand, an increase in the frequency of irregularity increases the magnitudes of WSS extrema while bringing the peaks closer together. Further, a positive correlation is found between the degree of irregularity as well as the number of locations of elevated LSC. The presence of irregularity creates additional vortices in the upstream section of the stenosis. Both the upstream and downstream sections of the stenosis are subjected to the opposing shear-layers with higher magnitudes, which may lead to endothelial damage. Finally, the shear-thinning effect of blood is studied using the power-law model. The magnitudes of the maxima and minima in WSS have a lower value for the shear-thinning model than the Newtonian case. Also, the vortices that were produced in the upstream section because of the irregularity get suppressed by the shear-thinning effect of the blood. © 2021 Author(s).