© 2018, The Author(s). Searching for new Higgs particle beyond the observed light Higgs boson h0(125 GeV) will unambiguously point to new physics beyond the standard model. We study the resonant production of a CP-even heavy Higgs state H0 in the di-Higgs channel, gg → H0 → h0h0 → WW*WW*, at the LHC Run-2 and the high luminosity LHC (HL-LHC). We analyze two types of the 4W decay modes, one with the same-sign di-leptons (4W → ℓ±νℓ±ν4q) and the other with tri-leptons (4W → ℓ±νℓ∓νℓ±ν2q). We perform a full simulation for the signals and backgrounds, and estimate the discovery potential of the heavy Higgs state at the LHC Run-2 and the HL-LHC, in the context of generic two-Higgs-doublet models (2HDM). We determine the viable parameter space of the 2HDM as allowed by the theoretical constraints and the current experimental limits. We systematically analyze the allowed parameter space of the 2HDM which can be effectively probed by the heavy Higgs searches of the LHC, and further compare this with the viable parameter region under the current theoretical and experimental bounds.