Magnetic targeting drug delivery is a method of carrying drug-loaded magnetic nanoparticles to a tissue target in the human body under the applied magnetic field. This method increases the drug concentration in the target and reduces the adverse side-effects. In this article, a mathematical model is presented to describe the hydrodynamics of ferrofluids as drug carriers flowing in a blood vessel under the applied magnetic field. Numerical simulations are performed to obtain better insight into the theoretical analysis with computational fluid dynamics. A 3D flow field of magnetic particles in an idealised blood vessel model containing an aneurysm is analysed to further understand clinical application of magnetic targeting drug delivery. Simulation samples demonstrate the important parameters leading to adequate drug delivery to the target site depending on the applied magnetic field in coincidence with reported results from animal experiments. Results of the analysis provide the important information and can suggest strategies for improving delivery in favour of the clinical application.