The preparation of new palladium complexes in situ that were composed of a series of chiral diphosphite ligands, which were derived from (1S,2S)-trans-1,2-cyclohexanediol, have been described. It was found that (1S,2S)-bis[(S)-1,1′-binaphthyl-2,2′-diyl]phosphite-cyclohexanediol was the suitable ligand in the Pd-catalyzed allylic alkylation, and up to 75% ee for (E)-dimethyl 2-(1,3-diphenylallyl)malonate was obtained. In compared with the results of the asymmetric allylic alkylation, (1S,2S)-bis[(R)-1,1′-binaphthyl-2,2′-diyl]phosphite-cyclohexanediol was proved to be the most efficient ligand in the Rh-catalyzed asymmetric hydrogenation of dimethyl itaconate and enamides with up to 99% ee. The stereochemically matched combinations between the diol skeleton and diaryl moieties of the ligands were essential for inducing high enantioselectivities in the two transformations. It was found that the sense of the enantiodiscrimination of the products was mainly determined by the configuration of the binaphthyl phosphite moieties.