In this work, a new magnetic MNPs@SiO2@Propyl@AMP/Cu heterogeneous nanocatalyst by immobilization of copper complex on the surface of magnetic nanoparticles was designed and prepared. After that, the prepared organic-inorganic catalyst was evaluated by various identification techniques such as FT-IR, EDX, XRD, TGA, FESEM, and TEM, and the results showed that the desired structure was successfully prepared. Also, in order to investigate the efficiency of the MNPs@SiO2@Propyl@AMP/Cu nanocatalyst as a heterogeneous catalyst, it was used for green and one-pot synthesis of 3-amino-5-oxo-4-phenyl-4H,5H-pyrano[3,2-c]chromene-2-carbonitrile derivatives. The use of MNPs@SiO2@Propyl@AMP/Cu catalyst led to the synthesis of the desired derivatives with higher efficiency and shorter reaction time than previously reported works. In addition, the prepared MNPs@SiO2@Propyl@AMP/Cu nanocatalyst has the ability to be recycled and reused for 7 consecutive periods and has high stability, which is well consistent with the principles of green chemistry.