One-pot multicomponent reactions are an attractive synthetic strategy to generate multiple molecular scaffolds. Activation of a terminal alkyne C–H bond by transition metal catalysts is a reaction of fundamental interest in organic synthesis. One of the best examples of such a process is three components coupling of aldehydes, alkynes, and amines (A3-coupling). Herein, Cu(II)-containing nano-silica triazine based dendrimer was prepared, characterized and utilized as a retrievable catalytic system (Cu(II)-TrDen@nSiO2) for green formation of propargylamines under solvent-free conditions. The various aldehydes/ketones, amines, and phenylacetylene were reacted at 100 °C in the presence of the 1.34 mol% of the catalyst to synthesize propargylamines in high yields (87%–98%). The prepared catalyst can be isolated assisted by a simple filtration and recovered for five courses without significant reduction in its efficiency. The as-prepared nano-catalyst was characterized by FT-IR, TEM, SEM, EDX, TGA and ICP. Performing the reactions in environmentally friendly and affordable conditions, the low catalyst percentage, high yield of products, short reaction times and easy workup are the merits of this protocol.