  We present a static and axisymmetric traversable wormhole spacetime with
vanishing Arnowitt-Deser-Misner (ADM) mass which is characterized by a length
parameter $l$ and a deformation parameter $a$ and reduces to the massless Kerr
vacuum wormhole as $l\to 0$. The spacetime is analytic everywhere and
regularizes a ring-like conical singularity of the massless Kerr wormhole by
virtue of a localized exotic matter which violates the standard energy
conditions only near the wormhole throat. In the spherically symmetric case
($a=0$), the areal radius of the wormhole throat is exactly $l$ and all the
standard energy conditions are respected outside the proper radial distance
approximately $1.60l$ from the throat. While the curvature at the throat is
beyond the Planck scale if $l$ is identical to the Planck length $l_{\rm p}$,
our wormhole may be a semi-classical model for $l\simeq 10l_{\rm p}$. With
$l=10l_{\rm p}$, the total amount of the negative energy supporting this
wormhole is only $E\simeq -26.5m_{\rm p}c^2$, which is the rest mass energy of
about $-5.77\times 10^{-4}{\rm g}$. It is shown that the geodesic behavior on
the equatorial plane does not qualitatively change by the localization of an
exotic matter.
