The purpose of the present invention is to provide a method for efficiently producing an olefin (co)polymer containing a constituent unit derived from 1-butene, the (co)polymer having a molecular weight that is sufficiently high even for high temperature conditions that are beneficial for industrial production methods. This purpose can be achieved by means of a method for producing an olefin (co)polymer containing a constituent unit derived from 1-butene, wherein at least 1-butene and, if necessary, an α-olefin having 2 or more carbon atoms (excluding 1-butene) and other monomers are (co)polymerized in the presence of an olefin polymerization catalyst that contains (A) a crosslinked metallocene compound represented by general formula [I] and (B) at least one type of compound selected from among (b-1) an organic aluminum oxy compound, (b-2) a compound that forms an ion pair upon a reaction with the crosslinked metallocene compound (A), and (b-3) an organic aluminum compound, at a polymerization temperature of 55-200° C. and a polymerization pressure of 0.1-5.0 MPaG.