  Motivated by $-2 \sigma$ deviation from the Standard Model prediction for the
forward--backward asymmetry of $Z \to b \bar{b}$ decay in the LEP data, we
explore the anomalous couplings of $Z b \bar{b}$ vertex through the electroweak
precision test extended by including $A_{FB}^b$. We introduce a new variable
$\epsilon'_b$ to measure the anomalous right-handed coupling in $Z b \bar{b}$
vertex. Implications of our analysis on the nonuniversal contact interactions
are studied and the left-right model is also considered as a possible origin of
the anomalous right-handed couplings.
