Computer modeling and simulation is an effective tool to investigate, analyze, and understand the homodynamic, mechanical behavior of blood flow. The detailed information on shear stress, pressure drops, recirculation, stagnation, and turbulence can be applied in the medical practice to establish a direct linkage between flow characteristic and disease. In this paper, a novel gradient smoothing method is proposed to simulate the blood flow in the common artery, vessel with stenosis, and abdominal aortic aneurysm. Compared with the standard finite volume method, the gradient smoothing method is originated from the gradient smoothing operation to approximate the spatial derivatives at various locations based on irregular cells regardless its physical background. The dual time stepping scheme and point-implicit five-stage RungeKutta (RK5) method are implemented to enhance the efficiency and stability in iterative solution procedures. The numerical results have demonstrated that the model obtained from gradient smoothing method is more accurate than the standard finite volume method using commercial software of Fluent.