Catalytic asymmetric synthesis of GRL-06579A (1), an HIV-1 protease inhibitor effective against multi-protease-inhibitor-resistant viruses, is described. A convergent strategy that utilizes heterobimetallic multifunctional catalysts developed in our group is a key feature of the synthesis. The chirality of the bicyclic tetrahydrofuran unit of 1 was introduced through Al-Li-bis(binaphthoxide) (ALB) catalyst-controlled Michael addition of dimethyl malonate to racemic 4-O-protected cyclopentenone. ALB afforded not only the trans adduct with up to 96% ee from a matched substrate through kinetic resolution, but also the cis adduct with 99% ee through a catalyst-controlled Michael addition to a mismatched substrate. The Michael addition to produce the unusual cis adduct is described in detail. The framework of the bicyclic tetrahydrofuran was constructed by an intramolecular oxy-Michael reaction. The amino alcohol unit was constructed by an La-Li3-tris(binaphthoxide) (LLB)-catalyzed diastereoselective nitroaldol reaction of N-Boc aldehyde (Boc = tert-butoxycarbonyl) derived from L-phenylalanine. LLB promoted the nitroaldol reaction without racemization of the chiral aldehyde to give the nitroaldol adduct in 85% yield and with 93:7 diastereoselectivity and over 99% ee.