The study of electroweak boson pair production provides a powerful tool to search for new phenomena beyond the Standard Model (SM). Extra neutral vector bosons Z′ decaying to charged gauge vector boson pairs W + W - are predicted in many scenarios of new physics, including models with an extended gauge sector. The diboson production allows to place stringent constraints on the Z-Z′ mixing parameter ξ and Z′ mass, MZ′. We present the Z′ exclusion region in the ξ - MZ′ plane for the first time by using data comprised of pp collisions at s = 13 TeV and recorded by the ATLAS and CMS detectors at the CERN LHC, with integrated luminosities of 36.1 and 35.9 fb -1 , respectively. The exclusion region has been significantly extended compared to that obtained from the previous analysis performed with Tevatron data, as well as with LHC data collected at 7 and 8 TeV. Also, we found that these constraints on the Z-Z′ mixing factor are more severe than those derived from the global analysis of electroweak data. Further improvement on the constraining of this mixing can be achieved from the analysis of data to be collected at higher luminosity expected in Run II.