Catalytic asymmetric hydroboration of unsaturated bonds has been recognized as the most straightforward method for the construction of chiral organoboron compounds. Although catalytic asymmetric hydroboration of alkenes has been well-developed, enantioselective hydroboration of allenes still remains rare probably due to the challenges in controlling the enantio-, stereo-, and regioselectivity. Additionally, the hydroboration products might go through over-borohydride, making the catalytic asymmetric dihydroboration of allenes challenging. Here, we report a cobalt-catalyzed asymmetric dihydroboration of allenes using a ligand relay strategy with two simple ligands. This protocol shows excellent enantio-, stereo-, and regioselectivity with positive functional group compatibilities in the construction of chiral 1,4-diboronate products. The applications of this reaction are demonstrated by various product derivatizations, gram-scale reactions, and the preparation of artigenin analogues. Mechanistic studies indicate that the achiral ligand controls the first hydroboration of allenes, and the chiral oxazoline iminopyridine ligand is responsible for the subsequent isomerization and asymmetric hydroboration.