The invention provides a method for making carboxylic acid anhydride. In the method, carboxylic ether derived from alcohol and carboxylic acid, a small amount of hydrogen and carbon monoxide, which serve as raw materials, undergoes a carbonylation reaction in a liquid reaction medium in the presence of a VIIIB group catalyst to form carboxylic acid anhydride, wherein the reaction medium comprises the VIIIB group catalyst, an organic halide, a carboxylic ether, an alkali metal salt, carboxylic acid anhydride, carboxylic acid and at least one kind of ion liquid consisting of cations and anions; the cation in the ionic liquid has a nitrogen-containing heterocyclic structure; and the ionic liquid may have at least one of the following four structural forms (I, II, III and IV). The method accelerates oxonation speed by adopting the specific ionic liquid cocatalyst.