In this research work, the prediction of the diffusion coefficient (Dp) of Irganox® 1076 (Ir‐76) antioxidant in HDPE‐based food contact packaging films was carried out. The diffusion of this additive was studied both, in neat HDPE film and in HDPE nanocomposites films made of HDPE matrix filled with 1, 3, and 5 wt% of a commercially available organoclay (Cloisite®15A). The diffusion experiments were carried out by using the Roe's method on films consisting of a stack of several polymer films having a total nominal thickness of 120 ± 01 μm. Diffusion coefficients were determined in the temperature range 80°C to 100°C according to the second Fick's law by measuring the evolution of the Ir‐76 concentration in the films by means of Fourier transform infrared (FTIR) spectroscopy analysis. The results indicated that the diffusion coefficient of Ir‐76 in HDPE films decreased with the addition of the organoclay, and a maximum reduction of 78% (at 23°C) in the diffusion rate of the Ir‐76 was observed at an optimum filler content of 3 wt%, thus making these films attractive for the plastic packaging industry.