In the present article we study the energy levels of a 2D hydrogenic atom when a constant magnetic field is applied. We compute the energy spectrum with the help of a generalization of the mesh point technique recently proposed by Schwartz. We also estimate, via a variational method, the upper energy bound for small and large values of the external magnetic field. We show that the results obtained by O Mustafa (1993 J. Phys.: Condens. Matter 5 1327) have to be modified in the weak-magnetic-field regime.