A highly efficient Rh-catalyzed asymmetric hydrogenation of rigid cyclic 3-amino-4-alkyl/aryl disubstituted maleimides has been developed for the first time by using 5,5'-bridged axially chiral biaryl diphosphine ligands (BridgePhos), whose dihedral angle can be controlled by modifying the length of the 5,5'-bridging chain. Both 4-aryl and alkyl-substituted substrates exhibit outstanding catalytic behavior using the BridgePhos-Rh catalyst with the most suitable dihedral angle, enabling the construction of chiral disubstituted succinimides with excellent yields (up to 99%) and stereoselectivities (up to 99% ee and >20:1 dr). Mechanistic studies based on the control experiments and DFT calculations indicated that the two added hydrogen atoms of the products originate from two different H2 molecules and the hydrogenation proceeds via a H2 σ-bond metathesis pathway for the alkane release in the hydrogenation cycle. This protocol can be performed on a gram-scale with a low catalyst loading (S/C = 5000) and allows stereodivergent access to all four stereoisomers. The resulting hydrogenation products offer several potential transformations, including the first asymmetric catalytic synthesis of moxifloxacin hydrochloride, a novel fluoroquinolone antibiotic developed by Bayer Pharmaceuticals, with high efficiency.