  We revealed the detailed structure of a vastly extended H$\alpha$-emitting
nebula ("H$\alpha$ nebula") surrounding the starburst/merging galaxy NGC 6240
by deep narrow-band imaging observations with the Subaru Suprime-Cam. The
extent of the nebula is $\sim$90 kpc in diameter and the total H$\alpha$
luminosity amounts to $\approx 1.6 \times 10^{42}$ erg s$^{-1}$. The volume
filling factor and the mass of the warm ionized gas are
$\sim$10$^{-4}$--10$^{-5}$ and $\sim$$5 \times 10^8$ $M_\odot$, respectively.
The nebula has a complicated structure, which includes numerous filaments,
loops, bubbles, and knots. We found that there is a tight spatial correlation
between the H$\alpha$ nebula and the extended soft X-ray-emitting gas, both in
large and small scales. The overall morphology of the nebula is dominated by
filamentary structures radially extending from the center of the galaxy. A
large-scale bi-polar bubble extends along the minor axis of the main stellar
disk. The morphology strongly suggests that the nebula was formed by intense
outflows - superwinds - driven by starbursts. We also found three bright knots
embedded in a looped filament of ionized gas that show head-tail morphologies
in both emission-line and continuum, suggesting close interactions between the
outflows and star forming regions. Based on the morphology and surface
brightness distribution of the H$\alpha$ nebula, we propose the scenario that
three major episodes of starburst/superwind activities which were initiated
$\sim$10$^2$ Myr ago formed the extended ionized gas nebula of NGC 6240.
