In this paper, an efficient method for the synthesis of 2-amino-5-oxo-5,6,7,8-tetrahydro-4H-chromene derivatives is described. The method uses Fe3O4 magnetic nanoparticles coated with poly (ε-caprolactone)/poly (ethylene glycol)/poly (ε-caprolactone) (MNPs-Fe3O4/PCL–PEG–PCL) as a biodegradable and green catalyst under solvent-free conditions. The catalyst was prepared from PCL–PEG–PCL copolymer and MNPs-Fe3O4 and characterized by FT-IR, X-ray diffraction and SEM spectroscopy. Most aromatic aldehydes bearing electron-withdrawing or electron donating groups reacted successfully with malononitrile and dimedone under solvent-free conditions at 80 °C. The corresponding chromenes were isolated in good to excellent yields and the structures of them were confirmed by 1H NMR and IR spectroscopy. The catalyst could be recovered using an external magnet without a considerable loss in its catalytic activity. Moreover, some advantages of this method are simplicity of procedure, easy separation of the catalyst, high yields, efficiency, stability and non-toxicity of the catalyst, short reaction times, and environmentally benign conditions.