Provided is graphene-embraced particulate for use as a lithium-ion battery anode active material, wherein the particulate comprises primary particle(s) of an anode active material and multiple sheets of a first graphene material overlapped together to embrace or encapsulate the primary particle(s) and wherein a single or a plurality of graphene-encapsulated primary particles, along with an optional conductive additive, are further embraced or encapsulated by multiple sheets of a second graphene material, wherein the first graphene and the second graphene material is each in an amount from 0.01% to 20% by weight and the optional conductive additive is in an amount from 0% to 50% by weight, all based on the total weight of the particulate. Also provided are an anode and a battery comprising multiple graphene-embraced particulates.