We discuss a particular d-dimensional Gauss Bonnet-dilatonic universe compactified on S1 motivated from M-theory. We examine the time-evolution of the dynamical equations where many interesting consequences are revealed and discussed in some details. Under reasonable conditions, the discussed model can provide a mechanism to realize, in higher-dimensions (d>4), the accelerated expansion of the universe in the presence of dark energy, without the presence of phantom energy and without the contraction of some inteal dimension.