Catalyzes the stepwise hydrogenation of geranylgeraniol to phytol during chlorophyll A (ChlA) biosynthesis. 3 NADP(+) + phytyl diphosphate = geranylgeranyl diphosphate + 3 H(+) + 3 NADPH Porphyrin-containing compound metabolism; chlorophyll biosynthesis. Belongs to the geranylgeranyl reductase family. ChlP subfamily.