  We consider static spherically symmetric wormhole configurations in a
gravitational theory of a scalar field with a potential $V(\phi)$ and
nonminimal derivative coupling to the curvature describing by the term
$(\epsilon g_{\mu\nu} + \kappa G_{\mu\nu}) \phi^{,\mu}\phi^{,\nu}$ in the
action. We show that the flare-out conditions providing the geometry of a
wormhole throat could fulfilled both if $\epsilon=-1$ (phantom scalar) and
$\epsilon=+1$ (ordinary scalar). Supposing additionally a traversability, we
construct numerical solutions describing traversable wormholes in the model
with arbitrary $\kappa$, $\epsilon=-1$ and $V(\phi)=0$ (no potential). The
traversability assumes that the wormhole possesses two asymptotically flat
regions with corresponding Schwarzschild masses. We find that asymptotical
masses of a wormhole with nonminimal derivative coupling could be positive
and/or negative depending on $\kappa$. In particular, both masses are positive
only provided $\kappa<\kappa_1\le0$, otherwise one or both wormhole masses are
negative. In conclusion, we give qualitative arguments that a wormhole
configuration with positive masses could be stable.
