  We give a characterizaion of Gorenstein toric Fano $n$-folds with index
$n-1$, which is called Gorenstein toric Del Pezzo $n$-folds, among toric
varieties. In practice, we obtain a condition for a lattice $n$-polytope to be
a Gorenstein Fano polytope. In our proof, we do not use Batyrev-Juny's
classification of Gorenstein Fano polytopes.
