The staghorn fern genus Platycerium is one of the most commonly grown ornamental ferns, and it evolved to occupy a typical pantropical intercontinental disjunction. However, species-level relationships in the genus have not been well resolved, and the spatiotemporal evolutionary history of the genus also needs to be explored. Plastomes of all the 18 Platycerium species were newly sequenced. Using plastome data, we reconstructed the phylogenetic relationships among Polypodiaceae members with a focus on Platycerium species, and further conducted molecular dating and biogeographical analyses of the genus. The present analyses yielded a robustly supported phylogenetic hypothesis of Platycerium. Molecular dating results showed that Platycerium split from its sister genus Hovenkampia ~35.2 million years ago (Ma) near the Eocene-Oligocene boundary and began to diverge ~26.3 Ma during the late Oligocene, while multiple speciation events within Platycerium occurred during the middle to late Miocene. Biogeographical analysis suggested that Platycerium originated in tropical Africa and then dispersed eastward to southeast Asia-Australasia and westward to neotropical areas. Our analyses using a plastid phylogenomic approach improved our understanding of the species-level relationships within Platycerium. The global climate changes of both the Late Oligocene Warming and the cooling following the mid-Miocene Climate Optimum may have promoted the speciation of Platycerium, and transoceanic long-distance dispersal is the most plausible explanation for the pantropical distribution of the genus today. Our study investigating the biogeographical history of Platycerium provides a case study not only for the formation of the pantropical intercontinental disjunction of this fern genus but also the 'out of Africa' origin of plant lineages.