Using polymeric composite incorporated transition metal nanoparticles to promote various organic reactions has been found as one of the most powerful strategies in organic synthesis. In this paper, CuSO4 nanoparticles (CuSO4 NPs) anchored on the surface of polymeric composites comprising of water‐insoluble acidic poly (toluenesulfonic acid‐formaldehyde) (PTSAF) and water‐soluble basic polyethyleneimine (PEI) to form the desired PEI/PTSAF‐supported CuSO4 NPs catalyst (CuSO4NPs@PEI/PTSAF) have been fabricated. Characterization of the as‐synthesized catalyst by inductively coupled plasma (ICP), Fourier transform infrared (FTIR), X‐Ray diffraction (XRD), scanning electron microscopy (SEM), energy‐dispersive spectroscopy (EDX) and elemental mapping analysis, transmission electron microscopy (TEM), and thermogravity analysis (TGA) demonstrated successful immobilization of the CuSO4 NPs on the PEI/PTSAF composite. This novel catalyst was highly active in the one‐pot A3 and decarboxylative A3 coupling reactions toward generating corresponding propargylamines in good to excellent yields under solvent‐free reaction. The nature of the well distribution of CuSO4 NPs coordinated with PEI ligand in the CuSO4NPs@PEI/PTSAF composite leads to superior catalytic activity. The present methodology offers several advantages such as high catalytic activity, good to excellent yields, short reaction times, simple operations, compatibility of broad scope of substrates, and environmental friendliness. More importantly, the catalyst can be easily recovered from the reaction mixture by a simple filtration and still exhibits remarkable reusability with only marginal loss of its performance after five consecutive runs.