  We investigate the shear viscosity of thermalized photons in the quark gluon
plasma (QGP) at weak coupling and $\mathcal{N}=4$ super Yang-Mills plasma
(SYMP) at both strong and weak couplings. We find that the shear viscosity due
to the photon-parton scattering up to the leading order of electromagnetic
coupling is suppressed when the coupling of the QGP/SYMP is increased, which
stems from the blue-shift of the thermal-photon spectrum at strong coupling. In
addition, the shear viscosity rapidly increases near the deconfinement
transition in a phenomenological model analogous to the QGP.
