A method for producing an olefin polymer, in which an olefin compound is polymerized in the presence of a Lewis acid catalyst at a temperature of 0° C. or lower to obtain an olefin polymer, the method comprising a step of feeding a raw material liquid including the olefin compound to a reactor provided with a cooling unit, a step of polymerizing the olefin compound in the reactor to obtain a reaction liquid including the olefin polymer, a deactivation step of adding a deactivator to the reaction liquid taken out from the reactor to deactivate the Lewis acid catalyst, and a step of supplying the reaction liquid after the deactivation step to a cold recovery unit to recover cold from the reaction liquid, wherein the amount of the Lewis acid catalyst is 0.5×10−3 to 1.0×10−1 mol % based on the total amount of the olefin compound.