A novel heterogeneous catalyst, CuI supported on sulfur functionalized halloysite (CuI@HNTs-S), was designed and synthesized through functionalization of the halloysite nanoclay surface with 3-mercaptopropyl trimethoxysilane and subsequent immobilization of CuI. The catalyst was characterized by using various characterization techniques such as FTIR, SEM/EDS, XRD, ICP and TGA. The catalytic activity of CuI@HNTs-S for the synthesis of propargylamines through ultrasonic-assisted multi-component A3 coupling reaction of aldehydes, phenyl acetylene and amines was also studied. The results established that CuI@HNTs-S could efficiently catalyze the reaction to furnish the desired products in excellent yield and in short reaction time. Notably the catalyst was recyclable and could be recycled with slight loss of the catalytic activity for five reaction runs. Then, the ability of pristine HNTs and sulfur functionalized HNTs toward CuI grabbing was compared quantitatively using molecular simulation. Calculated energies confirmed better performance of HNTs-S toward CuI physisorption, which decreases its leaching during catalytic reaction. This result was experimentally confirmed by observing the superior recyclability and low copper leaching of CuI@HNTs-S compared to CuI@HNTs.