Recently, conceptually new physics beyond the Standard Model has been proposed, where a hidden conformal sector provides "unparticle" which couples to the Standard Model sector through higher dimensional operators in low energy effective theory. Among several possibilities, we focus on operators involving unparticle, the Higgs doublet and the gauge bosons. Once the Higgs doublet develops the vacuum expectation value, the conformal symmetry is broken and as a result, the mixing between unparticle and Higgs boson emerges. We find that this mixing can cause sizable shifts for the couplings between Higgs boson and a pair of gluons and photons, because these couplings exist only at the loop level in the Standard Model. These Higgs couplings are the most important ones for the Higgs boson search at the CERN Large Hadron Collider, and the unparticle physics effects may be observed together with the discovery of Higgs boson. (C) 2008 Elsevier B.V. All rights reserved.