A composite composition for electrochemical cell electrode applications, the composition comprising multiple solid particles, wherein (a) a solid particle is composed of graphene platelets dispersed in or bonded by a first matrix or binder material, wherein the graphene platelets are not obtained from graphitization of the first binder or matrix material; (b) the graphene platelets have a length or width in the range of 10 nm to 10 μm; (c) the multiple solid particles are bonded by a second binder material; and (d) the first or second binder material is selected from a polymer, polymeric carbon, amorphous carbon, metal, glass, ceramic, oxide, organic material, or a combination thereof. For a lithium ion battery anode application, the first binder or matrix material is preferably amorphous carbon or polymeric carbon. Such a composite composition provides a high anode capacity and good cycling response. For a supercapacitor electrode application, the solid particles preferably have meso-scale pores therein to accommodate electrolyte.