Abstarct: In this study, rising bubble and falling ferrofluid droplet in nonmagnetic viscous fluid under the magnetic field in two-phase flow is studied. For this approach, lattice Boltzmann method, baxsed on pseudo-potential model, was used. The related computer code was validated for two-phase flows. Then, three different problems were considered. First, rising bubble behavior in viscous fluid was simulated. Three different regimes, namely: spherical, ellipsoidal, and spherical-cap, were observed. In the second part of this work, ferrofluid droplet behavior in nonmagnetic viscous fluid, under uniform magnetic field, was studied. A hybrid lattice Boltzmann-finite volume method was applied to simulate the effect of magnetic field on falling ferrofluid droplet in a non-magnetic viscous fluid. Lattice Boltzmann method was used to track the moving interface between the two immiscible phases and to update the flow field by adding the magnetic field force. The magnetic induction equation was solved using finite volume method. The effects of the magnetic Bond number, susceptibility and magnetic field direction on deformation of the falling droplet were investigated in details. The related results reveal that increase in the magnetic Bond number or susceptibility leads to a larger deformation of the droplet. Also; in horizontal magnetic field, the falling process takes more time in compared to the vertical magnetic field. Moreover, the local distribution of surface tension force and magnetic force around the falling droplet is analyzed. As the third part of this research, ferrofluid droplet behavior in nonmagnetic viscous fluid, under nonuniform magnetic field, was investigated. The related results reveal that applying external nonuniform magnetic field is an effective and contactless way to control the droplet movment. At the end, rising bubble from the needle tip under non uniform magnetic field were investigated. Results showed that, by appling suitable magnetic field deattachment of the bubble are occurred faster. Generally, it is found that the developed hybrid multiphase Lattice Boltzmann/finite-volume method is a suitable approach for simulation of falling ferrofluid droplet under uniform magnetic field.