An alkali metal sulfonate-substituted binaphthyl-phosphine transition metal complex is disclosed, which is represented by formula (I)[M(X).sub.n (Q)(SO.sub.3 A--BINAP)]Y (I)wherein M represents a transition metal atom; SO.sub.3 A--BINAP represents a tertiary phosphine represented by formula (II) ##STR1## in which A represents an alkali metal atom; X represents a chlorine atom, a bromine atom, or an iodine atom;when n is 1, M represents ruthenium, Q represents benzene or p-cymene, and Y represents a chlorine atom, a bromine atom, or an iodine atom;when n is 0 and M is iridium or rhodium, Q represents 1,5-cyclo-octadiene or norbornadiene, and Y represents ClO.sub.4, PF.sub.6 or BF.sub.4 ; and when n is 0 and M is palladium, Q represents .pi.-allyl, and Y represents ClO.sub.4, PF.sub.6, or BF.sub.4. A method of enantioselectively hydrogenating an olefin, a ketone, or an imine, which comprises carrying out the enantioselective hydrogenation using as a catalyst the alkali metal sulfonate-substituted binaphthylphosphine transition metal complex represented by formula (I) is also disclosed.