In this research, the mechanical and thermal properties of nanocomposites containing alumina nanoparticles in the highdensity polyethylene/recycled polyethylene terephthalate/maleic anhydride polyethylene (HDPE/rPET/MAPE) matrix were investigated. For this purpose, tensile, flexural, impact energy, and differential scanning calorimetry (DSC) test were done. Here, 0, 1, 3, and 5 wt% alumina nanoparticles were added to the HDPE/rPET/MAPE using a co-rotating screw extruder. Morphological studies using scanning electron microscopy revealed that alumina nanoparticles within HDPE/rPET/MAPE matrix were well dispersed in low content of nanoparticles (up to 3 wt%). The results of mechanical tests showed that the presence of alumina nanoparticles improved tensile strength, elastic modulus, flexural strength, and impact energy. The maximum improvement was observed for the sample containing 3 wt% of alumina. DSC test revealed alumina nanoparticles in the content of 3 wt% increased the crystallinity degree of HDPE in the blend of HDPE/rPET/MAPE and caused to approach the melting points of HDPE and rPET.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.