The motion and shape of a ferrofluid droplet placed in a non-magnetic viscous fluid and driven by a magnetic field are modeled numerically. The governing equations are the Maxwell equations, momentum equation and incompressibility. The numerical simulation uses a volume-of-fluid algorithm with a continuum-surface-force formulation for an axisymmetric geometry. The deformations in the drop under non-uniform magnetic fields are simulated. Droplets exhibit shape changes along the applied magnetic field. We have found that the ferrofluid droplet forms a prolate ellipsoid in the presence of a non-uniform magnetic field. For higher magnetic field strengths, the droplet undergoes dramatic deformation. This in turn influences the motion of the droplet through the viscous medium.