  We report on the discovery of an infrared cometary nebula around PSR
J1549$-$4848 in our Spitzer survey of a few middle-aged radio pulsars.
Following the discovery, multi-wavelength imaging and spectroscopic
observations of the nebula were carried out. We detected the nebula in Spitzer
IRAC 8.0, MIPS 24 and 70 $\mu$m imaging and in Spitzer IRS 7.5--14.4 $\mu$m
spectroscopic observations, and also in the WISE all-sky survey at 12 and 22
$\mu$m.These data were analyzed in detail, and we find that the nebula can be
described with a standard bow-shock shape, and that its spectrum contains
polycyclic aromatic hydrocarbon and H$_2$ emission features. However, it is not
certain which object drives the nebula. We analyze the field stars and conclude
that none of them can be the associated object because stars with a strong wind
or mass ejection that usually produce bow shocks are much brighter than the
field stars. The pulsar is approximately 15\arcsec\ away from the region in
which the associated object is expected to be located. In order to resolve the
discrepancy, we suggest that a highly collimated wind could be emitted from the
pulsar and produce the bow shock. X-ray imaging to detect the interaction of
the wind with the ambient medium and high-spatial resolution radio imaging to
determine the proper motion of the pulsar should be carried out, which will
help verify the association of the pulsar with the bow shock nebula.
