Extra scalar fields are common in beyond Standard Model (SM) new physics, and they may mix with the 125 GeV SM-like Higgs boson discovered at the LHC. This fact suggests possible discovery channels for these new scalar fields with their decay modes involving the 125 GeV Higgs boson. In this work, we explore the LHC search potential of the heavy CP-even Higgs boson H in the two-Higgs-doublet model. We focus on the channel of H decaying to a pair of light CP-even Higgs bosons h, with two h's decaying to two b jets and diphoton sequentially. This channel is particularly involved when the relevant cubic coupling is enhanced. We find such enhancement to be possible when taking a large CP-odd Higgs mass input for the two-Higgs-doublet model spectrum. Analogous to the SM Higgs self-coupling measurement, the two b jets plus diphoton final states are of particular interest due to the manageable SM background. After performing a cut-based analysis of both signal and background processes, we demonstrate the LHC search sensitivities for the heavy CP-even Higgs boson in a broad mass range via the two b jets plus diphoton final states.