The present article reports the preparation of high density polyethylene (HDPE)/sepiolite-clay nanocomposites with improved mechanical performance and melt extensional properties by melt compounding using a co-rotating twin screw extruder. Maleic anhydride grafted high density polyethylene (HDPE-g-MA) (having different MFI and maleic anhydride content) was used as compatibiliser to investigate systematically the effect of polarity and molecular weight on the properties of HDPE/sepiolite nanocomposites. The influence of sepiolite loading (1–10 wt%) and type of compatibilizer on morphological, mechanical and melt extensional properties (melt strength, drawability and extensional viscosity) were investigated and analyzed. Sepiolite-clay significantly enhanced the mechanical properties, melt strength and extensional viscosity with slight reduction in drawability at 10% w/w loading. For example, ∼40% increase in tensile modulus and ∼50% improvement in flexural modulus was obtained at 10% w/w sepiolite loading. The compatibiliser having lower MFI showed significant improvement in melt extensional properties as compared to compatibiliser having higher MFI. Scanning electron microscopy and transmission electron microscopy revealed the better dispersion of sepiolite in the presence of compatibiliser, however it was much better when HDPE-g-MA having higher MFI was used as compared to compatibiliser having lower MFI. Thermal stability increased in the presence of sepiolite which was further improved in the presence of compatibiliser.