Method for producing propylene-based polymer

A method for producing a propylene-based polymer, including polymerizing propylene or propylene and an α-olefin except propylene in the presence of a catalyst with a horizontal polymerization reactor equipped with stirring vanes rotating around a horizontal axis therein by a continuous vapor-phase polymerization, which removes heat of polymerization by heat of vaporization of a liquefied propylene, wherein the reactor can set a plurality of area sections different in temperature in a horizontal direction inside the reactor, and satisfies at least one of i) a temperature difference, T1=Tω−Tα, between an area section including an upstream end of the reactor (Tα) and a downstream end (Tω) thereof is 0.1 to 20° C. and ii) a temperature difference, T2=Tx−Tz, between an area section including a catalyst feed part (Tx) and dew point (Tz) of a mix gas in the reactor is 0 to 5° C.