We study a model of scalar field with a general non-minimal kinetic coupling to itself and to the curvature, as a source of dark energy, and analyze the cosmological dynamics of this model and the issue of accelerated expansion. Solutions giving rise to power-law expansion have been found. The dynamical equation of state is studied for the two cases, without and with free kinetic term . In the first case, a behavior very close to that of the cosmological constant was found. In the second case, a solution was found, which match the current phenomenology of the dark energy. The model shows a rich variety of dynamical scenarios.