  We show that in Gauss-Bonnet gravity with negative Gauss-Bonnet coefficient
and without a cosmological constant, one can explain the acceleration of the
expanding Universe. We first introduce a solution of the Gauss-Bonnet gravity
with negative Gauss-Bonnet coefficient and no cosmological constant term in an
empty $(n+1)$-dimensional bulk. This solution can generate a de Sitter
spacetime with curvature $n(n+1)/\{(n-2)(n-3)|\alpha|\}$. We show that an
$(n-1)$-dimensional brane embedded in this bulk can have an expanding feature
with acceleration. We also considered a 4-dimensional brane world in a
5-dimensional empty space with zero cosmological constant and obtain the
modified Friedmann equations. The solution of these modified equations in
matter-dominated era presents an expanding Universe with negative deceleration
and positive jerk which is consistent with the recent cosmological data. We
also find that for this solution, the $"n"th$ derivative of the scale factor
with respect to time can be expressed only in terms of Hubble and deceleration
parameters.
