  We study the expansion law of the universe dominated by the oscillating
scalar field with non-minimal derivative coupling to gravity as G^{\mu \nu}
\partial_{\mu} \phi \partial_{\nu} \phi. In this system the Hubble parameter
oscillates with a frequency of the effective mass of the scalar field, which
formerly caused a difficulty in analyzing how the universe expands. We find an
analytical solution for power law potentials and interpret the solution in an
intuitive way by using a new invariant of the system. As a result, we find
marginally accelerated expansion for the quadratic potential and no accelerated
expansion for the potential with higher power.
