  There exist many observational evidences implying the expansion of our
universe is undergoing a late-time acceleration, the mechanism of this
acceleration is yet unknown. In the so-called thick brane model this phenomena
is attributed to the thickness of the brane along the extra dimension. In this
study we mainly rely to the consistency of this model with most recent
observational data related to the background evolution. The new Supernova Type
Ia (SNIa) Gold sample and Supernova Legacy Survey (SNLS) data, the position of
the acoustic peak at the last scattering surface from the WMAP observations and
the baryon acoustic oscillation peak found in the Sloan Digital Sky Survey
(SDSS) are used to constrain the free parameter of the thick codimension 1
brane model. To infer its consistency with age of our universe, we compare the
age of old cosmological objects with what computed using the best fit values
for the model parameters. When the universe is matter dominated, $w=0$, at 68%
level of confidence, the combination of Gold sample SNIa, CMB shift parameter
and SDSS databases provides $\Omega_m=0.31_{-0.02}^{+0.02}$,
$\Omega_{\cal{C}}=0.05_{-0.01}^{+0.01}$, $w_r=-1.40_{-0.20}^{+0.20}$, hence a
spatially open universe with $\Omega_k=0.21_{-0.08}^{+0.08}$. The same
combination with SNLS supernova observation gives
$\Omega_m=0.28_{-0.02}^{+0.03}$, $\Omega_{\cal{C}}=0.037_{-0.004}^{+0.003}$,
$w_r=-2.05_{-0.15}^{+0.15}$ consequently provides a spatially open universe
$\Omega_k=0.11_{-0.07}^{+0.10}$. These results obviously seem to be in
contradiction with the most recent WMAP results indicating a flat universe.
