A ruthenium-phosphine complex represented by formula (I)[RuX.sub.l (L).sub.m (R-BINAP)]Y.sub.n (I)wherein R-BINAP represents a tertiary phosphine represented by formula (II): ##STR1## wherein R represents a hydrogen atom or a methyl group; X represents a halogen atom; L represents substituted or unsubstituted benzene or acetonitrile; Y represents a halogen atom, CLO.sub.4, PF.sub.6, BPh.sub.4 (wherein Ph represents a phenyl group) or BF.sub.4 ; when L is substituted or unsubstituted benzene, l represents 1, m represents 1, and n represents 1; and whe L is acetonitrile, when l is 1, then m represents 2, and n represents 1, and when l is 0, the m represents 4, and n represent 2. The complex exhibits excellent catalytic activity in asymmetric reactions to provide a product of high optical purity. The complex can be produced at low cost.