Although morphology-controlled metal nanocatalysts supported on graphene sheets are promising, highly effective catalysts for various electrochemical reactions, their preparation is still challenging. In this paper, we report a facile method for preparing structures with highly branched Pd nanodendrites (PdNDs) supported on graphene nanoplatelets (GNPs) (PdNDs-GNP) and their application as a cathode catalyst in a nonaqueous Li-O-2 battery. PdNDs formed on the GNP sheets via a particle-attachment mechanism had an average size of approximately 14 nm, strongly anchored on the GNP sheets, and were well distributed. Binder-free, flexible PdNDs-GNP/graphene oxide (GO) paper electrodes were fabricated and used in a nonaqueous Li-O-2 battery. Because of the high catalytic activity of the PdNDs-GNP structures, the Li-O-2 cell using the PdNDs-GNP/GO paper electrode exhibited substantially lower overpotentials both on discharge and charge compared with those of the GNP/GO paper electrode without Pd nanocatalysts and even those of the paper electrode consisting of irregularly shaped Pd nanoparticles supported on GNP (PdNPs-GNP) and GO. We found that Li2O2 formed on the PdNDs-GNP/GO paper electrode had a sheet-like morphology, which decomposed more efficiently than did the large toroidal product formed on the GNP/GO paper electrode. Consequently, the Li-O-2 cell using the PdNDs-GNP/GO paper electrode exhibited greatly enhanced cyclability over 30 cycles as compared with that of the GNP/GO paper electrode (15 cycles).