Abstract: For a non-homogeneous metric measure space satisfying the upper doubling and the geometrically doubling conditions, the Herz-Morrey-Hardy spaces on the non-homogeneous metric measure spaces are introduced. The decomposition of the Herz-Morrey-Hardy spaces is discussed. Then, as an application, by the properties of the non-homogeneous metric measure spaces, based on the theory of boundedness for Calderón-Zygmund operators on L^q spaces, the boundedness of the Calderón-Zygmund operators from the Herz-Morrey-Hardy spaces into the Morrey-Herz spaces with non-homogeneous metric measure is obtained.