The present study explains the preparation of high-density polyethylene (HDPE)-based nanocomposites containing different amounts of montmorillonite (MMT) nanoclay (1–10 wt%). These nanocomposites were obtained by melt blending in a co-rotating twin screw extruder in absence and presence of a compatibiliser (HDPE-g-MA). The melt rheological behaviour of HDPE/MMT nanocomposites has been investigated by using capillary rheometer at 190°C, 200°C and 210°C over the shear rate range of 50–1000 s−1. The melt viscosity of HDPE increased marginally at 10 wt% filler loading while addition of compatibiliser to HDPE/MMT composites did not show any significant effect on viscosity. All nanocomposites showed shear thinning and non-Newtonian flow behaviour. The power law index reduced with increase in MMT concentration and increased with increase in temperature while opposite trend was observed for the consistency index. The activation energy was highest for the nanocomposites containing 10 wt% MMT and decreased upon addition of coupling agent.