  With the assumption that the dominant diagram in supersymmetry for the
spin-independent cross section of the dark matter particle is due to Higgs
boson exchange, we obtain an upper limit on the Higgs-dark-matter coupling
based on the new result of the CDMSII Collaborations. We then obtain an upper
limit on the invisible width of the Higgs boson, numerically it is less than
20-120 MeV for $m_h \simeq 120 - 180$ GeV. Implications for Higgs boson search
are also discussed.
