A new magnetic nanocatalyst, namely [Fe3O4@SiO2@RNMe2-SO3H][CF3CO2] (FSRNSC), was fabricated, and characterized using FT-IR, EDS (energy-dispersive X-ray spectroscopy), elemental mapping, FE-SEM (field-emission scanning electron microscopy), XRD (X-ray diffraction), VSM (vibrating-sample magnetometry), TG (thermogravimetric) and DTG (differential thermogravimetric) analyses. It was utilized as a highly effectual and magnetically recoverable catalyst for the construction of pyrimido[4,5-b]quinolines (12 examples) in high yields (15−50 min) and short times (88−96%). The synthesis was performed through the one-pot, three-component reaction of aryl aldehydes, dimedone, and 6-amino-1,3-dimethyluracil in the absence of solvent.