Recently, graphene nanoplatelets (GNPs) or silicon nitride (Si$_3$N$_4$) may be employed as a reinforcing element in the Al2024 aluminium alloy matrix due to the solid lubricant property of GNPs and high compressive strength of Si$_3$N$_4$. However, there is no article related to the investigation of the mechanical properties of Al2024–Si$_3$N$_4$–graphene hybrid composites. In this article, Si$_3$N$_4$ or Si$_3$N$_4$/graphene binary particle-reinforced Al2024 aluminium-based composites were produced by powder metallurgy route and induction heat-treatment process. The effects of induction heat treatment (a 500°C sintering temperature and a 35 MPa pressure), Si$_3$N$_4$ (1–12 wt%) and graphene (0.15–0.45 wt%) contents on the microstructure and mechanical strength of Al-based composites were examined. According to the test results, the micro Vickers hardness improved from ${\sim}$94.8 HV (Al2024 alloy) to ${\sim}$105.2 HV (Al2024–9Si$_3$N$_4$) and ${\sim}$108.5 HV (Al2024–9Si$_3$N$_4$–0.15GNPs). Similarly, the compressive strength was enhanced from ${\sim}$361 MPa (Al2024 alloy) to ${\sim}$510 MPa (Al2024–9Si$_3$N$_4$) and ${\sim}$610 MPa (Al2024–9Si$_3$N$_4$–0.15GNPs). The compressive strength of sintered and induction heat-treated Al2024–9Si$_3$N$_4$–0.15GNPs composite improved by ${\sim}$8.9% compared with the conventional sintered same specimen’s strength. In conclusion, the induction heat-treatment process and Si$_3$N$_4$/graphene addition significantly enhanced the mechanical strength of Al2024 hybrid composites.