Method for producing foam molded article and foam molded article

A method for producing a foam-molded article for continuously molding a foam-molded article including continuously repeating the following step 1, step 2, step 3 and step 4 in this order, wherein the step1 includes melting a resin composition containing a liquid crystalline polyester, the step 2 includes introducing a supercritical fluid which is non-reactive with the liquid crystalline polyester in the supercritical state and is a gas at normal temperature and normal pressure into the resin composition by introduction device in an amount of 0.1 parts by mass or more and 0.3 parts by mass or less with respect to 100 parts by mass of the liquid crystal polyester, and melt-kneading, the step 3 includes injecting the resin composition containing the supercritical fluid after melt-kneading into a mold, and step 4 includes producing a foamed molded article by foaming by lowering at least one of the pressure and temperature of the supercritical fluid contained in the resin composition to below the critical point of