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The vector boson scattering (VBS) processes at the Large Hadron Collider (LHC) are very suitable to probe the anomalous quartic gauge couplings (aQGCs). We study the dimension-8 operators contributing to the anomalous γγWW coupling via the exclusive γγ→W+W− scattering. By analysing the kinematical features of the signals, we propose an event selection strategy to highlight the aQGC contributions. The statistical significances of the signals at 13 and 14 TeV LHC with current luminosity are obtained. The γγ→W+W− scattering is found to be sensitive to OMi operators and can contribute to the combined limits.