Abstract: The method of dimerization of alpha-olefins consists in mixing at least one alpha-olefin with a two-component catalyst consisting of organic compounds of titanium, having the general formula Ti (OR).sub.4, and of aluminum, having the general formula AlR.sub.3, where R is an alkyl having from 1 to 6 carbon atoms, or an aryl, in a medium of a hydrocarbon solvent, at a temperature of 0.degree. to 100.degree. C and a pressure from 1 to 30 atm. Said constituents of the catalyst are pretreated with an ethylene-hydrogen mixture, containing from 5 to 95 percent by volume of hydrogen, at a temperature of from 0.degree. to 100.degree. C and a pressure of the ethylene-hydrogen mixture from 0.2 to 15 atm., for a period of time from 1 to 120 minutes. The method ensures high yields of butene-1 and hexenes, and high selectivity of the catalyst to said products. The butene-1 content of the butane mixture obtained in the process of ethylene dimerization is as high as 99 percent.