  We consider static spherically symmetric solutions in the scalar-tensor
theory of gravity with a scalar field possessing the nonminimal kinetic
coupling to the curvature. The lagrangian of the theory contains the term
$(\varepsilon g^{\mu\nu}+\eta G^{\mu \nu})\phi_{,\mu}\phi_{,\nu}$ and
represents a particular case of the general Horndeski lagrangian, which leads
to second-order equations of motion. We use the Rinaldi approach to construct
analytical solutions describing wormholes with nonminimal kinetic coupling. It
is shown that wormholes exist only if $\varepsilon=-1$ (phantom case) and
$\eta>0$. The wormhole throat connects two anti-de Sitter spacetimes. The
wormhole metric has a coordinate singularity at the throat. However, since all
curvature invariants are regular, there is no curvature singularity there.
