There is provided an optically active copper catalyst composition comprising (a) an optically active salicylideneaminoalcohol represented by the formula (1): ##STR00001## wherein R.sup.1 and R.sup.2 are the same or different, and independently represent a substituted or unsubstituted lower alkyl group, a substituted or unsubstituted aralkyl group, or a substituted or unsubstituted aryl group; X.sup.1 and X.sup.2 are the same or different, and independently represent a hydrogen atom, a lower alkoxy group, a nitro group, a lower alkoxycarbonyl group, a cyano group or a halogen atom; and * represents an asymmetric center, provided that both of X.sup.1 and X.sup.2 don't represent hydrogen atoms, (b) a monovalent or divalent copper compound, and (c-1) a lithium compound or (c-2) a compound selected from aluminum compounds having Lewis acidity, titanium compounds having Lewis acidity, boron compounds having Lewis acidity, zirconium compounds having Lewis acidity and hafnium compounds having Lewis acidity; and a process for producing an optically active cyclopropane compound by using the same.