  The latest CDF anomaly, the excess of dijet events in the invariant-mass
window 120-160 GeV in associated production with a $W$ boson, can be explained
by a baryonic $Z'$ model in which the $Z'$ boson has negligible couplings to
leptons. Although this $Z'$ model is hardly subject to the Drell-Yan constraint
from Tevatron, it is constrained by the dijet data from UA2 ($\sqrt{s} = 630$
GeV), and the precision measurements at LEP through the mixing with the SM $Z$
boson. We show that under these constraints this model can still explain the
excess in the M_{jj} \sim 120 - 160 GeV window, as well as the claimed cross
section $\sigma(W Z') \sim 4$ pb. Implications at the Tevatron would be the
associated production of $\gamma Z',\; Z Z'$, and $Z'Z'$ with the $Z' \to jj$.
We show that with tightened jet cuts and improved systematic uncertainties both
$\gamma Z' \to \gamma jj$ and $Z Z' \to \ell^+ \ell^- j j$ channels could be
useful to probe this model at the Tevatron.
