  We have studied the torsion cosmology model in Kaluza-Klein theory. We
considered two simple models in which the torsion vectors are
$A_{\mu}=(\alpha,0,0,0)$ and $A_{\mu}=a(t)^2(0,\beta,\beta,\beta)$,
respectively. For the first model, the accelerating expansion of the Universe
can be not explained without dark energy which is similar to that in the
standard cosmology. But for the second model, we find that without dark energy
the effect of torsion can give rise to the accelerating expansion of the
universe and the alleviation of the well-known age problem of the three old
objects for appropriated value of the model parameter $\beta$. These
outstanding features of the second torsion cosmology model have been supported
by the Type Ia supernovae (SNIa) data.
