Motivated by the recent result reported from LHC on the di-photon search from the Standard Model (SM) Higgs boson, we obtain limits on the anomalous couplings Hγγ and HZγ. We also perform a calculation at tree level of the decay widths as well as of the branching ratios for the reactions H → γγ and H → Zγ in the context of effective lagrangian for Higgs boson masses 115 ≤ M H ≤ 130 GeV. We find that the decay widths and branching ratios from these reactions enhanced significantly due to the anomalous Hγγ and HZγ vertex, which would lead to measurable effects in Higgs signals at the LHC. Moreover, our results complement other studies on the channels H → γγ and H → Zγ.