  We propose a model of dark energy consists of a single scalar field with a
general non-minimal kinetic couplings to itself and to the curvature. We study
the cosmological dynamics of the equation of state in this setup. The coupling
terms have the form $\xi_{1} R f(\phi)\partial_{\mu}\phi\partial^{\mu}\phi$ and
$\xi_{2} R_{\mu\nu}f(\phi)\partial^{\mu}\phi\partial^{\nu}\phi$ where $\xi_{1}$
and $\xi_{2}$ are coupling parameters and their dimensions depend on the type
of function $f(\phi)$. We obtain the conditions required for phantom divide
crossing and show numerically that a cosmological model with general
non-minimal derivative coupling to the scalar and Ricci curvatures can realize
such a crossing.
