Mixed matrix membranes (MMMs) based on the polymer of intrinsic microporosity PIM-1 and the zeolitic imidazolate framework ZIF-8 were prepared and their permeation and sorption properties investigated. Self-supported films with ZIF-8 contents up to 43 vol% were studied using GC gas permeation apparatus and a McBain sorption microbalance. Permeability coefficients were determined for the following set of gases: He, H2, O2, N2, CO2, CH4. For “as-cast” films, an increase in ZIF-8 loading results in increases in the permeability and diffusion coefficients as well as in the separation factors α(H2/N2), α(H2/CH4), α(He/N2), α(O2/N2) and α(CO2/CH4). For all ZIF-8 contents studied, permeability is enhanced by treatment with ethanol. Data points on several Robeson diagrams are located above the 2008 upper bound. Free volume in MMMs containing ZIF-8 was studied using positron annihilation lifetime spectroscopy (PALS) and radio thermoluminescence (RTL) methods. It was shown that the introduction of ZIF-8 nanoparticles into the PIM-1 matrix results in an increase in free volume which may be assumed to arise from a combination of the contributions cavities and of more loosely packed polymer chains at the boundary between ZIF-8 particles and the PIM-1 matrix. The results obtained for the PIM-1/ZIF-8 MMMs are compared with literature data for other MMMs.