Thermodynamic stability boundary of structure-H hydrates with large guest species and methane (CH4) at extremely high pressures has been almost unclear. In the present study, the four-phase equilibrium relations in the structure-H CH4 + 1,1,2,2,3,3,4-heptafluorocyclopentane (1,1,2,2,3,3,4-HFCP) mixed hydrate system were investigated in a temperature range of (281.05 to 330.12) K and a pressure range up to 373 MPa. The difference between equilibrium pressures in the structure-H CH4 + 1,1,2,2,3,3,4-HFCP mixed hydrate system and the structure-I simple CH4 hydrate system gets larger with increase in temperature. The structure-H CH4 + 1,1,2,2,3,3,4-HFCP mixed hydrate survives even at 330 K and 373 MPa without any structural phase transition. The maximum temperature where the structure-H CH4 + 1,1,2,2,3,3,4-HFCP mixed hydrate is thermodynamically stable is likely to be beyond that of the structure-H simple CH4 hydrate.