  We report results of $^{12}$CO ($J=1$-0) mapping observations of the
Wolf-Rayet starburst galaxy Mrk 1259 which has optical evidence for the
superwind seen from a nearly pole-on view. The CO emission is detected in the
central 4 kpc region. The nuclear CO spectrum shows a blue-shifted ($\Delta V
\simeq -27$ km s$^{-1}$) broad (FWHM $\simeq$ 114 km s$^{-1}$) component as
well as the narrow one (FWHM $\simeq 68$ km s$^{-1}$). The off-nuclear CO
spectra also show the single-peaked broad component (FWHM $\simeq$ 100 km
s$^{-1}$). The single-peaked CO profiles of both the nuclear and off-nuclear
regions may be explained if we introduce a CO gas disk with a velocity
dispersion of $\sim 100$ km s$^{-1}$. If this gas disk would be extended up to
a few kpc in radius, we may explain the wide line widths of the off-nuclear CO
emission. Alternatively, we may attribute the off-nuclear CO emission to the
gas associated with the superwind. However, if all the CO gas moves along the
biconical surface of the superwind, the CO spectra would show double-peaked
profiles. Hence, the single-peaked CO profiles of the off-nuclear regions may
be explained by an idea that the morphology and/or velocity field of the
molecular-gas superwind are more complex as suggested by hydrodynamical
simulations.
