The magnetic liquids such as ferrofluids, biocompatible magnetic nanocarrier, play an important role as drug carriers in the human body. Based on Maxwell's equation and Navier-Stokes equations, a time-dependent analysis of a twodimensional computational model of magnetic fluid flow is purposed. The FEM is applied to solve Maxwell's equation for a static magnetic field and Navier-Stokes equations for fluid dynamics. The result of magnetic field has some influences to ferrofluid dynamic flow in blood vessel.