The magnetically separable Au NPs–Fe₃O₄–rGO catalyst provides a robust and efficient route for the A³ coupling reaction of secondary amines, terminal alkynes and aldehyde with tolerance of diverse functional groups for the synthesis of propargylamine in high yields. Further, the catalyst could be reused several times without losing significant activity due to the stability of the NPs onto reduced graphene oxide sheets (rGO). The synthesized catalyst was characterized by different instrumental techniques before as well as after the catalytic reaction and it was observed that the catalyst retained its size and surface morphology after the reaction. The advantages of using the Au NPs–Fe₃O₄–rGO catalyst for the synthesis of pharmaceutically important compounds, propargylamines, over those in previous reports include its magnetically separable nature, additive-free characteristic, functional group tolerance and recyclability. The enhanced catalytic activity of the Au NPs–Fe₃O₄–rGO composite material results from the synergistic effect among Au NPs, Fe₃O₄ NPs and rGO sheets.