In this work, a stabilized formulation to solve the inductionless magnetohydrodynamic (MHD) problem using the finite element method is presented. The important feature of this formulation resides in the design of the stabilization terms, which serve several purposes. First, convective dominated flows in the Navier-Stokes equations can be dealt with. Second, there is no need to use interpolation spaces subject to an inf-sup condition both for the pairs u-p and j- and therefore linear interpolation spaces can be used. Finally, this formulation allows to deal with flows with high values of the Hartmann number, that is, flows where the electromagnetic forces are much higher than the viscous forces.