We describe Galadi speciosus, gen. et sp nov., the second peramelemorphian (Yarala burchfieldi being the first) to be described from Oligo-Miocene deposits of Riversleigh World Heritage Property, northwestern Queensland. G. speciosus is represented by relatively complete craniodental material, including an exceptionally well-preserved skull. This taxon exhibits several apomorphies that clearly place it in the order Peramelemorphia, but it appears to be more plesiomorphic than any modern bandicoot. We present the first morphological phylogenetic analyses of Peramelemorphia, using 51 craniodental characters. Our analyses recover Yarala and Galadi speciosus outside crown group Peramelemorphia, with G. speciosus weakly supported as the sister taxon of the crown group. The craniodental morphology of G. speciosus, particularly its robust skull and proportionately short and broad snout, suggests that it filled a different ecological niche to extant bandicoots. We hypothesize that G. speciosus occupied a predominantly faunivorous, dasyurid-like niche in the Oligo-Miocene rainforests of Riversleigh, at a time when dasyurids appear to have been relatively rare.