Since the flow of a magnetic fluid could easily be influenced by an external magnetic field, its hydrodynamic modeling promises to be useful for magnetically controllable delivery systems. It is desirable to understand the flow fields and characteristics before targeted magnetic particles arrive at their destination. In this study, we perform an analysis for the effects of particles and a magnetic field on biomedical magnetic fluid flow to study the targeted magnetic-particle delivery in a blood vessel. The fully developed solutions of velocity, flow rate, and flow drag are derived analytically and presented for blood with magnetite nanoparticles at body temperature. Results reveal that in the presence of magnetic nanoparticles, a minimum magnetic field gradient (yield gradient) is required to initiate the delivery. A magnetic driving force leads to the increase in velocity and has enhancing effects on flow rate and flow drag. Such a magnetic driving effect can be magnified by increasing the particle volume fraction.