A simple and efficient synthesis of 3,4-dihydropyrimidinones or thiones is described, using silica-supported perchloric acid ($HClO_4-SiO_2$) as a heterogeneous catalyst from an aldehyde, $eta$-dicarbonyl compound, and urea or thiourea under solvent-free conditions. Compared to the classical Biginelli reactions, this method consistently has the advantage of high yields, short reaction time, easy separation, and tolerance towards various functional groups.