In the present work, a three-dimensional characteristic-based off-lattice Boltzmann method is developed in cylindrical coordinates to simulate physiological blood flow through the pathological arteries. The singular point that arises at the center of the axis, r=0 in cylindrical coordinates is avoided using the azimuthal mapping approach. A special periodic boundary condition in the azimuthal direction is developed that redefines the coordinates and the treatment of scalar and vector quantities across the periodic boundary is presented. The solver could also handle the body-fitted, curvilinear and non-uniform meshes through the Jacobian coordinate transformation. The developed solver is first verified for steady flow through a stenosed lumen and for spatially developing pulsatile flow through an abdominal aortic aneurysm using reference data from the literature. Thereafter, blood flow through a model irregular arterial stenosis is studied and the effects of the amplitude and frequency of irregularity, the Reynolds number, and the Womersley number on the flow dynamics are systematically investigated. The flow characteristics are analyzed using wall shear stress (WSS), divergence of WSS, oscillatory shear index (OSI), relative residence time (RRT) and the turbulence kinetic energy. Overall, the developed solver demonstrates the importance of shape of the stenosis on the blood flow dynamics for physiological inflow conditions.