  With the help of the Seiberg-Witten map, one can obtain an effective action
of a deformed QED from a noncommutative QED. Starting from the deformed QED, we
investigate the propagation of photons in the background of electromagnetic
field, up to the leading order of the noncommutativity parameter. In our
setting (both the electric and magnetic fields are parallel to the coordinate
axis $x^1$ and the nonvanishing component of the noncommutativity parameter is
$\theta^{23}$), we find that the electric field has no effect on the
propagation of photons, but the velocity of photons can be larger than the
speed of light ($c=1$) when the propagating direction of photons is
perpendicular to the direction of background magnetic field, while the
light-cone condition does not change when the propagating direction is parallel
to the background magnetic field. The causality associated with the
superluminal photons is discussed briefly.
