Abstract: We discuss a scenario of the type-II two-Higgs- doublet model (2HDM) in which the b (b) over bar gamma gamma rate of the Higgs pair production is enhanced due to the two nearly degenerate 125 GeV Higgs bosons ( h, H). Considering various theoretical and experimental constraints, we figure out the allowed ranges of the trilinear couplings of these two Higgs bosons and calculate the signal rate of b (b) over bar gamma gamma from the productions of Higgs pairs (hh, hH, HH) at the large hadron collider (LHC). We find that in the allowed parameter space some trilinear Higgs couplings can be larger than the Standard Model (SM) value by an order and the production rate of b _ b.. can be greatly enhanced. We also consider a “decoupling” benchmark point where the light CP-even Higgs has a SM-like cubic self-coupling while other trilinear couplings are very small. With a detailed simulation on the b (b) over bar gamma gamma signal and backgrounds, we find that in such a “decoupling” scenario the hh and hH channels can jointly enhance the statistical significance to 5 sigma at 14 TeV LHC with an integrated luminosity of 3000 fb(-1).