The augment of heat transfer and fluid of buoyancy-driven flow of Fe3O4-Water nanofluid in a square cavity under the influence of an external magnetic field is studied numerically. Cold temperature is applied on the side (vertical) walls and high temperature is imposed on the bottom wall while the top wall is kept at thermally insulated. The governing non-dimensional differential equations are solved using Marker and Cell (MAC) Algorithm. The developed MATLAB code is validated with previous literature and it gives good agreement. The effects of Rayleigh number Ra, Prandtl number Pr and Hartmann number Ha on the flow and heat transfer characteristics are analyzed. Results indicate that the temperature gradient is an increasing function of the buoyancy force. The heat transfer characteristics and flow behavior are presented in the form of streamlines and isotherms. The position of magnetic wire is played a vital role in controlling of heat transfer rate.