  We show that a Z' with suppressed couplings to the electron compared to the
Z-boson, with couplings to the b-quark, and with a mass close to the mass of
the Z-boson, provides an excellent fit to forward-backward asymmetry of the
b-quark and R_b measured on the Z-pole and $\pm 2$ GeV off the Z-pole, and to
A_e obtained from the measurement of left-right asymmetry for hadronic final
states. It also leads to a significant improvement in the total hadronic cross
section on the Z-pole and R_b measured at energies above the Z-pole. In
addition, with a proper mass, it can explain the excess of $Zb\bar b$ events at
LEP in the 90-105 GeV region of the $b\bar b$ invariant mass.
