We study the new physics related to the recent discovered 125 GeV Higgs by employing an important subset of the standard model gauge invariant dimension-six operators constructed by the the SM Higgs and gauge fields. Explicitly, we perform a model-independent calculation on the production and decays of the Higgs, the electric dipole moments (EDM) of the neutron and the electron, as well as the anomalous magnetic dipole moments of muon and electron. We find that, even all Higgs decay channels agree with the SM predictions, the SM theoretical uncertainties provide a lot of room to host NP associated with the 125 GeV boson. The neutron and electron EDM further severely constrain the relevant Wilson coefficients. The CP property associated with Higgs is also discussed in this work.