The Large Hadron Collider has recently discovered a Higgs-like particle having a mass around 125 GeV and also indicated that there is an enhancement in the Higgs to diphoton decay rate as compared to that in the standard model. We have studied implications of these discoveries in the bilinear R-parity violating supersymmetric model, whose main motivation is to explain the nonzero masses for neutrinos. The R-parity violating parameters in this model are Ïμ and bÏμ, and these parameters determine the scale of neutrino masses. If the enhancement in the Higgs to diphoton decay rate is true, then we have found Ïμ0.01 GeV and bÏμ∼1 GeV2 in order to be compatible with the neutrino oscillation data. Also, in the above mentioned analysis, we can determine the soft masses of sleptons (m L) and CP-odd Higgs boson mass (mA). We have estimated that mL300 GeV and mA700 GeV. We have also commented on the allowed values of Ïμ and bÏμ, in case there is no enhancement in the Higgs to diphoton decay rate. Finally, we present a model to explain the smallness of Ïμ and bÏμ. © 2013 American Physical Society.