  Double Field Theory (DFT) is a low-energy effective theory of a manifestly
$O(D,D)$ invariant formulation of the closed string theory when toroidally
compactified dimensions are present. The theory is based on a doubled spacetime
structure and, in order to preserve the gauge symmetry provided by the
invariance under generalized diffeomorphisms, a constraint has to be imposed on
fields and gauge parameters. In this paper, we propose a DFT-inspired
Supergravity by using a suitable {\em star product} that implements such
constraint and the corresponding algebraic structure is explored. We get a
consistent DFT in which also an orthogonality condition of momenta is necessary
for having a closed gauge algebra. In constructing this theory, we start from
the simplest case of doubling one spatial dimension where the action is
uniquely determined, without ambiguities, by the gauge symmetry. Then, the
extension to the generic $O(D, D)$ case is presented. The result is consistent
with the closed string field theory.
