A hidden fastener screen installation system is disclosed which includes a plurality of screen frame extrusions cooperating to form an opening across which a screen is positioned, wherein each screen frame extrusion defines at least one mounting surface configured to receive a plurality of mechanical fasteners to retain the screen frame extrusion to a portion of a building structure, and wherein at least one mounting rib extends outwardly from the mounting surface. The system further includes a trim mold defining a channel configured to closely receive and retain the mounting rib, wherein the screen is received in the channel and is retained by cooperation between the trim mold and the mounting rib, and wherein a portion of the trim mold is configured to extend over the fasteners such that the fasteners are hidden upon installation of the trim mold on the screen frame.