A method for producing an aromatic compound polymer comprising oxidatively polymerizing one or more of aromatic compound(s) having two or more hydrogen atoms directly connected to aromatic ring(s), in the presence of an oxidizing agent, wherein the method employs a catalyst composed of a transition metal complex or a catalyst prepared from a transition metal complex and an activating agent, and said catalyst has a parameter P defined by the following formula (A) of 0.50 or more, and a parameter Eo defined by the following formula (B) of 0.50 [V] or more: P=Af/Ai  (A) and Eo=(Epa+Epc)/2 [V]  (B).