  Applying the parametrization of dark energy density, we can construct
directly independent-model potentials. In Born-Infeld type phantom dark energy
model, we consider four special parametrization equation of state parameter.
The evolutive behavior of dark energy density with respect to red-shift $z$,
potentials with respect to $\phi$ and $z$ are shown mathematically. Moreover,
we investigate the effect of parameter $\eta$ upon the evolution of the
constructed potential with respect to $z$. These results show that the
evolutive behavior of constructed Born-Infeld type dark energy model is quite
different from those of the other models.
