Two intrinsically microporous polyimides (PIM-PIs) were synthesized by the polycondensation reaction of 4,4′-(hexafluoroisopropylidene)diphthalic anhydride (6FDA) and 3,3,3′,3′-tetramethylspirobisindane-6,7,6′,7′-tetracarboxylic dianhydride (SBI) with a newly designed o-hydroxyl-functionalized Tröger’s base diamine, 1,7-diamino-6H,12H-5,11-methanodibenzo[1,5]diazocine-2,8-diol (HTB). Both amorphous PIM-PIs were soluble in aprotic solvents and showed excellent thermal stability with onset decomposition temperature of ∼380 °C. SBI-HTB displayed a higher CO2 permeability (466 vs 67 barrer) than 6FDA-HTB but a significantly lower selectivity for CO2/CH4 (29 vs 73), H2/CH4 (29 vs 181), O2/N2 (4.6 vs 6.0), and N2/CH4 (1 vs 2.5). 6FDA-HTB displayed the highest gas-pair permselectivity values of all reported OH-functionalized PIM-PIs to date. The high permselectivity of 6FDA-HTB resulted primarily from exceptional diffusion selectivity due to strong size-sieving properties caused by hydrogen bonding between the proton of the hydroxyl group and the nitrogen atoms in the tertiary amine of the Tröger’s base (O–H···N).