Abstract: For a non-homogeneous metric measure space satisfying the upper doubling and the geometrically doubling conditions, the molecular Herz-Morrey-Hardy spaces on the non-homogeneous metric measure space are introduced. The decomposition of the molecular Herz-Morrey-Hardy spaces is discussed. Then, by the properties of the non-homogeneous metric measure space, the characteristics of atom block and molecule block, and the properties of discrete coefficients, the equivalent for the atomic Herz-Morrey-Hardy spaces and the molecular Herz-Morrey-Hardy spaces is proved. In nother words, this is the molecular characterization of the Herz-Morrey-Hardy spaces on non-homogeneous metric measure space.