Objective: The objective in the present investigation is to study the effect of magnetic field on thermal convection of an Oldroydian viscoelastic fluid through a Brinkman porous medium. Methods: The normal mode method is used to obtain the dispersion relation. Conclusions: For the case of stationary convection, Oldroydian viscoelastic fluid behaves like an ordinary Newtonian fluid and medium permeability and medium porosity have destabilizing effects on the system whereas the magnetic field and Darcy-Brinkman number have stabilizing effects on the system. It is also found that the modes may be oscillatory and non-oscillatory and the principle of exchange of stabilities is valid under certain condition.