Provided is a method of producing a composite metal oxide including, to calcine a composition containing an alkali metal and obtain a composite metal oxide, calcining the composition while being arranged on a mount a part of which in contact with the composition is formed of a metal oxide component. The metal oxide component has a content of K atoms ranging from 5 to 13 parts by weight in terms of K2O with respect to 100 parts by weight of the metal oxide component, and a total content of Al atoms, Zr atoms, Mg atoms, and Ce atoms ranging from 15 to 70 parts by weight in terms of oxides with respect to 100 parts by weight of the metal oxide component. The present invention thus provides a method of producing a composite metal oxide containing an alkali metal with reduced production costs.