  The Standard Model prediction on the forward-backward asymmetry for $b\bar b$
production ($A^b_{FB}$) is well consistent with the data of LEP I at the
Z-pole, but deviates from the data at $\sqrt s=89\; 93$ GeV which are slightly
away from the pole. This deviation implies that there still is room for new
physics. We calculate the $A^b_{FB}$ at vicinity of Z-pole in the Little Higgs
Model as well as other measurable parameters such as $R_b$ and $R_c$, by which
we may constrain the parameter space of the Little Higgs Model. This can be
tested in the newly proposed tera-Z factory. With the fitted parameters we
further make predictions on $A^b_{FB}$ and $A^t_{FB}$ for $t\bar t$ production
at the ILC energy.
