  We present a fit to precision electroweak data in the standard model extended
by an additional vector boson, Z', with suppressed couplings to the electron
compared to the Z boson, with couplings to the b-quark, and with mass close to
the mass of the Z boson. This scenario provides an excellent fit to
forward-backward asymmetry of the b-quark measured on the Z-pole and \pm 2 GeV
off the Z-pole, and to lepton asymmetry, A_e, obtained from the measurement of
left-right asymmetry for hadronic final states, and thus it removes the tension
in the determination of the weak mixing angle from these two measurements. 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. We explore in detail
properties of the Z' needed to explain the data and present a model for Z' with
required couplings. The model preserves standard model Yukawa couplings, it is
anomaly free and can be embedded into grand unified theories. It allows a
choice of parameters that does not generate any flavor violating couplings of
the Z' to standard model fermions. Out of standard model couplings, it only
negligibly modifies the left-handed bottom quark coupling to the Z boson and
the 3rd column of the CKM matrix. Modifications of standard model couplings in
the charged lepton sector are also negligible. It predicts an additional down
type quark, D, with mass in a few hundred GeV range, and an extra lepton
doublet, L, possibly much heavier than the D quark. We discuss signatures of
the Z' at the Large Hadron Collider and calculate the Z'b production cross
section which is the dominant production mechanism for the Z'.
