The first series of chiral phosphine-imidazole carbene ligands based on a 1,1'-binaphthyl framework were synthesized from (R)-2-amine-2'-(diphenylphosphino)-1,1'-binaphthyl (1) in a four-step pathway. After deprotonation of these phosphine-imidazolium salts with LiO(t)Bu, and subsequent complexation with [Ir(COD)Cl]2 and anion exchange with NaBArF, phosphine-carbene chelated iridium complexes (R)-6a and (R)-6b were obtained. Their structures have been characterized by NMR and X-ray diffraction analysis. The NHC-phosphine rhodium complex (R)-6c has been also obtained by a similar synthetic method. These iridium complexes have been applied to catalyze the asymmetric hydrogenation of alkenes to give the corresponding products in moderate to excellent conversion (up to 99%) and moderate enantioselectivities under mild conditions (up to 61% ee).