Catalysis using supported gold nanoparticles has attracted significant research interest due to their unique properties and potential that is directly related to their particle size. An efficient one-pot, three-component procedure is developed for the preparation of pyrimido[4,5- b][1,6]naphthyridin-4( 1H)-one derivatives (4a–h) by cyclocondensation of 6-amino-2-thioxo-2,3-dihydropyrimidin-4( 1H)-one (1), aromatic aldehydes (2), and 1-benzylpiperidin-4-one (3) in the presence of zeolite-nano Au as a green catalyst in ethanol at 80 °C. The presented methodology has a number of advantages including a reusable catalyst, easy access, short reaction times, high yields, and an easy work-up. The nanogold catalyst is characterized by X-ray diffraction and transmission electron microscopy. The structures of the prepared compounds are established by elemental analyses and spectral data (infrared, mass spectrometry, 1H, and 13C NMR). While molecular docking studies show that products 4a and 4c have binding affinities with the active site of CDKs. A bio-evaluation assay revealed that some of the products exhibit strong to moderate effects against proliferation of Huh7 in an in vitro model of human liver cancer cells as confirmed by morphological alteration. Compounds 4c and 4a offer the lowest IC50 values at 22.5 and 39 µM, respectively.