  We study the effects of dimension-six operators contributing to the $gt\bar
t$ vertex in top quark pair production at the Tevatron collider. We derive both
the limits from Run 1 data and the potential bounds from future runs (Run 2 and
3). Although the current constraints are not very strong, the future runs are
quite effective in probing these operators. We investigate the possibility of
disentangling different operators with the $t\bar t$ invariant mass
distribution and the top quark polarization asymmetry. We also study the
effects of a different set of operators contributing to single top production
via the $Wt\bar b$ coupling. We derive the current and potential future bounds
on these anomalous operators and find that the upgraded Tevatron can improve
the existing constraints from $R_b$ for one of the operators.
