Amberlyst A-21 supported CuI was found to be a highly efficient novel heterogeneous catalyst for the three-component reaction between amines, aldehydes and alkynes, commonly called A³-coupling. An environmentally benign, one-pot, A³-coupling reaction of various aldehydes, amines and terminal alkynes for the synthesis of propargylamine derivatives is here described. The developed protocol avoids the use of solvent and produces a variety of propargylamines in excellent yields within short reaction times. The catalyst can be easily prepared, recovered and reused for several times, without any appreciable loss in its activity.