In recent years, lasers have been widely used in the welding processes for automotive, aerospace, electrical and heavy manufacturing industries due to their high power density, small heat-affected zone and high productivity. Especially, with high depth-to-width ratio and high welding efficiency, keyholemode laser welding is more promising compared to the conventional welding processes. However, a number of defects, such as porosity, irregular beads, undercut and humping are frequently observed in laser welds, which deteriorates the strength and quality of the welded parts. In current study, an externally controllable electromagnetic force is introduced into the laser welding process to prevent porosity formation and to control weld bead shape. Numerical models are developed to study the transport phenomena in laser welding and to accurately calculate the current density and magnetic flux fields and the resulting electromagnetic forces in three-dimensional weldments. Effects of the electromagnetic force on metal flow, heat and mass transfer and weld bead shape are investigated. The continuum model is used to handle the entire domain including solid phase, liquid phase and mush zone. The enthalpy method is employed to handle the absorption and release of latent heat during melting and solidification. Inverse Bremsstrahlung (IB) absorption, Fresnel absorption and multiple reflections of laser beam energy at the keyhole walls are considered for the study of laser-plasma interaction. Volume of Fluid (VOF) technique is adopted to calculate the free surface evolution in the computation. As indicated by this study, porosity-free laser welds with desired bead shapes can be achieved with appropriate applications of electromagnetic forces.