Rosensweig’s modeling considers fluid dynamics, spins of ferromagnetic particles, magnetic polarization, and a magnetic induction field. The corresponding model incorporates the Navier-Stokes equations, the angular momentum equation, the magnetization equation, and the magnetostatic equation. In this talk, we propose linear, unconditionally energy-stable, and fully discrete finite element schemes for the model. We obtain the existence and uniqueness of the numerical solutions by the Leray-Schauder fixed point theorem, and prove the unconditional convergence through the Aubin-Lions-Simon lemma. Numerical experiments verify the effectiveness and accuracy of the schemes, and simulate the controllability of the magnetic fluid driven by an applied magnetic field.