Poly(4-methyl-1-pentene) (PMP) membranes were modified through isothermal annealing to investigate the change of their crystalline structure and rigid and mobile amorphous fractions (RAF and MAF), assuming a three-phase model, affected the gas transport behavior. The crystalline structure was characterized by wide-angle X-ray diffraction (WAXD) and small-angle X-ray scattering (SAXS) techniques, and the free volume properties were analyzed by positron annihilation lifetime spectroscopy. Compared with the pristine membrane, the annealed membranes show higher crystallinity; the crystals undergo partial structural change from form III to form I. The lamellar crystal thickness, rigid amorphous fraction thickness, and long period in the lamellar stacks increase with crystallinity. The annealed PMP membranes exhibit higher permeability due to the increase in larger size free volumes in MAF and higher selectivity due to the increase in smaller size free volumes in RAF, respectively. (C) 2016 Wiley Periodicals, Inc.