The annealing effect on coextruded linear low-density polyethylene (LLDPE) films has been investigated by positron annihilation lifetime spectroscopy (PALS). From the continuous positron lifetime distribution found for these films, the size distribution of the free-volume holes in the amorphous phase is calculated, as well as their fractional free volume. Also, diffusivity measurements at 298 K for He, O-2, and N-2 and X-ray diffraction measurements have been performed. The results reveal that annealing induces changes in the hole size distribution and in the amorphous fractional free volume of the films, along with an enhancement of the gas diffusivity. The correlation found between the amorphous fractional free volume and diffusion coefficients agrees with the free-volume model for diffusion in polymers. Moreover, the results show that the probability density function of the free-volume holes has certain influence on the diffusion coefficients, revealing that the impedance factors for diffusion would be controlled by the size distribution shape of the free-volume holes in the amorphous phase.