An object of the present invention is to provide an exhaust gas-purifying catalyst containing a composite oxide catalyst and a refractory support and being less prone to cause a decrease in its activity even when used at high temperatures in an atmosphere with high oxygen concentration. An exhaust gas-purifying catalyst includes a composite oxide catalyst containing rare-earth element, alkaline-earth element and precious metal, a part of the rare-earth element and a part of the alkaline-earth element forming composite oxide, and the composite oxide and a part of the precious metal forming solid solution, and a refractory support supporting the composite oxide catalyst and including at least one of a first composite oxide represented by a general formula AB2O4, a second composite oxide having perovskite structure represented by a general formula LMO3, and a third composite oxide having pyrochlore structure represented by a general formula X2Y2O7.