A dimer of a lower .alpha.-olefin is prepared by dimerizing a lower .alpha.-olefin in the presence of a catalyst comprising(A) nickel chloride,(B) a trialkylaluminum(C) at least one phosphorus compound selected from the group consisting of compounds of the formulae:PR.sup.1 R.sup.2 R.sup.3 (I)P(NR.sup.1.sub.2).sub.3 (II) andP(OR.sup.1).sub.3 (III) wherein R.sup.1, R.sup.2 and R.sup.3 are the same or different and each an alkyl group, a cycloalkyl group or a phenyl group and(D) 1,1,1,3,3,3-hexafluoroisopropanol,wherein the catalyst has improved activity because of the use of nickel chloride as a nickel component, so that the amounts of expensive trialkylaluminum and hexafluoroisopropanol can be decreased and the cost of the catalyst can be significantly reduced.