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We present a static and axisymmetric traversable wormhole spacetime withvanishing Arnowitt-Deser-Misner (ADM) mass which is characterized by a lengthparameter $l$ and a deformation parameter $a$ and reduces to the massless Kerrvacuum wormhole as $l\to 0$. The spacetime is analytic everywhere andregularizes a ring-like conical singularity of the massless Kerr wormhole byvirtue of a localized exotic matter which violates the standard energyconditions only near the wormhole throat. In the spherically symmetric case($a=0$), the areal radius of the wormhole throat is exactly $l$ and all thestandard energy conditions are respected outside the proper radial distanceapproximately $1.60l$ from the throat. While the curvature at the throat isbeyond 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 thiswormhole is only $E\simeq -26.5m_{\rm p}c^2$, which is the rest mass energy ofabout $-5.77\times 10^{-4}{\rm g}$. It is shown that the geodesic behavior onthe equatorial plane does not qualitatively change by the localization of anexotic matter.

Simple traversable wormholes violating energy conditions only near the Planck scale