This dissertation presents a search for lepton-flavor-violating (LFV) decays of the 125 GeV Higgs boson in final states of \mu\tau_{\mathrm{had}} and e\tau_{\mathrm{had}} in the full dataset collected by the ATLAS detector in 2012. The search is based on data samples of proton--proton collisions at \sqrt{s} = 8 TeV, corresponding to an integrated luminosity of 20.3 fb^{-1}. The topology of LFV events is exploited through an optimized selection of objects and events, with signal and control regions defined by event kinematics. A binned likelihood fit searching for the presence of LFV Higgs decays is performed using the reconstructed Higgs boson mass as the discriminating variable. No such decays are observed. The expected (observed) upper limits at 95% confidence on the branching ratios for the muon and electron final states are found to be Br(H \rightarrow \mu\tau) = 1.24% (1.85%) and Br(H \rightarrow e\tau) = 2.07% (1.81%).