We present the first attempt to access the x-dependence of the gluon unpolarized parton distribution function (PDF), based on lattice simulations using the large-momentum effective theory (LaMET) approach. The lattice calculation is carried out with pion masses of 340 and 678 MeV on a 2+1-flavor DWF configuration with lattice spacing a = 0.111 fm, for the gluon quasi-PDF matrix element with the nucleon momentum up to 0.93 GeV. Taking the normalization from similar matrix elements in the rest frame of the nucleon and pion, our results for these matrix elements are consistent with the Fourier transform of the global fit CT14 and PDF4LHC15 NNLO of the gluon PDF, within statistical uncertainty and the systematic one up to power corrections, perturbative O(αs) matching and the mixing from the quark PDFs. PACS numbers: 12.38.Mh, 25.75.Nq Introduction: The unpolarized parton distribution function (PDF) is the probability density for finding the corresponding parton with a certain longitudinal momentum fraction x in an infinite-momentum hadron at MS renormalization scale µ, that satisfies the hadron momentum sum rules,

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