  Motivated by the recent work of Zhang and Chen \cite{bin}, we generalize
their work to the non-minimally coupled case. We consider a quintom model of
dark energy with a single scalar field $T$ given by a Lagrangian which inspired
by tachyonic Lagrangian in string theory. We consider non-minimal coupling of
tachyon field to the scalar curvature, then we reconstruct this model in the
light of three forms of parametrization for dynamical dark energy.
