  We study cosmological evolution after inflation in models with non-minimal
derivative coupling to gravity. The background dynamics is solved and particle
production associated with rapidly oscillating Hubble parameter is studied in
detail. In addition, production of gravitons through the non-minimal derivative
coupling with the inflaton is studied. We also find that the sound speed
squared of the scalar perturbation oscillates between positive and negative
values when the non-minimal derivative coupling dominates over the minimal
kinetic term. This may lead to an instability of this model. We point out that
the particle production rates are the same as those in the Einstein gravity
with the minimal kinetic term, if we require the sound speed squared is
positive definite.
