Provided is a method of producing graphene from a microwave-expandable un-exfoliated graphite or graphitic carbon, comprising: (a) feeding a powder of the microwave-expandable material onto a non-metallic solid substrate, wherein the powder is in a ribbon shape having a first ribbon width and a first ribbon thickness; (b) moving the ribbon-shape powder into a microwave applicator chamber containing a microwave power zone having a microwave application width (no less than the first ribbon width) and a microwave penetration depth (no less than the first ribbon thickness) so that the entire ribbon-shape powder receives and absorbs microwave power with a sufficient power level for a sufficient length of time to exfoliate and separate the powder for producing graphene sheets; and (c) moving the graphene sheets out of the microwave chamber, cooling the graphene sheets, and collecting the graphene sheets in a collector container or for a subsequent use.