This invention relates to a method of preparing poly(alkylene carbonate) that has a molecular weight and polymer chain structure precisely controlled by adding a chain transfer agent composed of a compound having an alcohol or carboxylic acid functional group upon alternating copolymerization of an epoxide compound and carbon dioxide using a catalyst composed of a trivalent metal complex compound synthesized from a quaternary ammonium salt-containing Salen type ligand, and to a polymer compound prepared thereby. According to this invention, the polymer compound having a star-shaped chain as well as the polymer having a linear chain can be prepared. The low-molecular-weight poly(alkylene carbonate) has an —OH terminal group and can be used alone as a coating agent, etc., and also in mixtures with an isocyanate compound and thus can be easily utilized to prepare polyurethane.