A cost-effective and convenient method for supporting of Cu(II) nanoparticles on a modified chitosan backbone containing urea and thiourea bridges using thiosemicarbazide (TS), pyromellitic dianhydride (PMDA) and toluene-2,4-diisocyanate (TDI) linkers was designed. The prepared supramolecular (CS–TDI–PMDA–TS–Cu(II)) nanocomposite was characterized by using Fourier-transform infrared (FT-IR) spectroscopy, field emission scanning electron microscopy (FESEM), thermogravimetry/differential thermogravimetry analysis (TGA/DTA), energy-dispersive X-ray spectroscopy (EDS), EDS elemental mapping and X-ray diffraction (XRD). The obtained supramolecular CS–TDI–PMDA–TS–Cu(II) nanomaterial was demonstrated to act as a multifunctional nanocatalyst for promoting of multicomponent cascade Knoevenagel condensation/click 1,3-dipolar azide–nitrile cycloaddition reactions very efficiently between aromatic aldehydes, sodium azide and malononitrile under solvent-free conditions and affording the corresponding (E)-2-(1H-tetrazole-5-yl)-3-arylacrylenenitrile derivatives. Low catalyst loading, working under solvent-free conditions and short reaction time as well as easy preparation and recycling, and reuse of the catalyst for five consecutive cycles without considerable decrease in its catalytic efficiency make it a suitable candidate for the catalytic reactions promoted by Cu species.