The ATLAS and CMS collaborations reported the first signal of Lepton Flavor Violating (LFV) Higgs decay into tau and mu leptons. Standard Model forbids such processes at the renormalizable level because of lepton flavor symmetry. On the other hand, many extensions of the Standard Model do not exhibit such a symmetry and the models beyond the Standard Model (BSM) yield such processes. Hence, any signal for LFV processes can be interpreted as a direct probe for the BSM models. In this work, we consider LFV Higgs boson decays in a class of supersymmetric models including minimal supersymmetric extension of the SM (MSSM), Supersymmetric Type I Seesaw, and U(1)(B-L) extended MSSM supplied with the inverse seesaw mechanism for non-zero neutrino masses.