  We consider the cosmological application of Lee-Wick theory where a field has
a higher derivative kinetic operators. The higher derivative term can be
eliminated by introducing a set of auxiliary fields. We investigate the
cosmological evolutions of these fields as a candidate of dark energy. This
model has the same structure as so called ``quintom' model except the form of
potentials and the sign of the slope of the potentials. This model can give the
stable late time phantom dominated scaling solution ($\omega_{\DE} < -1$) or
tracking attractors ($\omega_{\DE} = 0$) depending on the choice of the slopes
of the potential. In order to be a viable dark energy candidate, the present
energy density contrast of dark energy ($\Omega_{\DE}^{(0)}$) should be close
to an observed value (0.73) at the same time. However, a simple toy model of
the theory can not satisfy both $\omega_{\DE}^{(0)} \simeq -1$ and
$\Omega_{\DE}^{(0)} = 0.73$. If we include the self interaction term of Lee
Wick field, then we are able to produce the observed values of those
quantities. However, in this case we are not be able to have the stable
solutions and we need to suffer from the fine tuning of its mass.
