A hybrid composite membrane material based on the PIM-1 polymer of intrinsic microporosity and MIL-101 nanoparticles of mesoporous chromium terephthalate has been prepared and tested. Fourier-transform IR spectroscopy has revealed the presence of interaction between the polymer matrix and the nanoparticles introduced into it. The addition of MIL-101 nanoparticles leads to an increase in the permeability and diffusion coefficients for gases (He, O-2, N-2, CO2) compared to the original polymer. Using positron annihilation lifetime spectroscopy (PALS), it has been shown that these changes result from an increase in the free volume in the polymer composite material.