  Once a parity is introduced in unparticle physics, under which unparticle
provided in a hidden conformal sector is odd while all Standard Model particles
are even, unparticle can be a suitable candidate for the cold dark matter (CDM)
in the present universe through its coupling to the Standard Model Higgs
doublet. We find that for Higgs boson mass in the range, 114.4 GeV < m_h < 250
GeV, the relic abundance of unparticle with mass 50 GeV < m_U < 80 GeV can be
consistent with the currently observed CDM density. In this scenario, Higgs
boson with mass m_h < 160 GeV dominantly decays into a pair of unparticles and
such an invisible Higgs boson may be discovered in future collider experiments.
