  We study the neutral Higgs boson production via the gluon fusion process with
the $\tautau$ final state at the upgraded Fermilab Tevatron, including a
complete simulation of signal channels and leading background processes. For
the SM Higgs boson, this $h\to \tautau$ channel may provide important addition
for the Higgs boson discovery in the mass range 120-140 GeV. In minimal
supersymmetric models, natural enhancement for the signal rate over the SM
expectation makes the $h,H,A\to \tautau$ signal observable for large
$\tan\beta$ and low $M_A$, which may lead to full coverage for SUSY Higgs
parameters at the Tevatron with a moderate integrated luminosity.
