  In this paper, we study the spherically symmetric traversable wormholes with
a scalar field supported by a phantom field in the anti-de Sitter (AdS)
asymptotic spacetime. Despite coupling the scalar matter field, these wormholes
remain massless and symmetric for reflection of the radial coordinate $r
\rightarrow -r$. The solution possesses a finite Noether charge $Q$, which
varies as a function of frequency $\omega$ with changes in the cosmological
constant $\Lambda$ and the throat size $r_0$. Under specific conditions, an
approximate ``event horizon'' will appear at the throat.
