The effects of organo-modified montmorillonite (OMMT) nanoclay and epoxidized natural rubber (ENR) content on the gas barrier, tensile, and the thermal properties of nanocomposite films based on low-density polyethylene (LDPE) are investigated. Linear low-density polyethylene-grafted maleic anhydride (LLDPE-g-MA) is used as a compatibilizer to obtain better dispersion of the nanoclay in the blends. The blends, with various amounts of ENR (0–10) wt%, are melt-compounded and extruded using a blown film extrusion single screw. The tensile properties of films are studied in machine direction (MD). The gas permeability of films is studied via constant pressure and a soap bubble flow meter. The melting and crystallization behaviors of films are examined via differential scanning calorimetry (DSC). Chemical interactions of composite blends are examined via Fourier transform infrared (FTIR) spectroscopy. An addition of 6 wt% nanoclay improved the tensile modulus by about 11 %. It further reduced the oxygen permeability by about 83 %. Although introducing OMMT decreased the percentage of crystallinity (XC), the presence of LLDPE-g-MA in the nanocomposite enhanced the property due to better intercalation between the phases. Incorporation of ENR caused an increase in the Young’s modulus for compatibilized nanocomposite systems, attributed to an interaction among clay, compatibilizer, and ENR, and cross-linking effects of ENR molecules. However, ENR decreased the permeability of the film due to the ability of amorphous regions to form crystallized structures during the blown process, and cross-linking effects of ENR. In addition, ENR reduced the XC of nanocomposites due to an interference that exists in the form of ENR molecular incorporation. The FTIR spectra showed that the maleic anhydride group in LLDPE-g-MA reacted in situ with the epoxy groups of ENR, which was an evidence of grafting reaction.