The energy and power requirements of portable electronic devices and electric vehicles are ever increasing, driving research into novel battery structures with increased volumetric energy and power densities. Existing energy storage technologies cannot satisfy both of these requirements. There are many reports on the application of graphene in batteries and supercapacitors with enhanced power and energy densities; however, few results were shown on the performance of an electrochemical energy storage device made of monolayer graphene. The energy storage capability of monolayer graphene is investigated in this paper and it can contribute an understanding of the application of graphene materials in high energy and power density batteries. In parallel, flexible solid-state batteries will relax design constraints, giving the freedom to create new device form factors. A mechanically flexible all-solid state battery can be made of monolayer graphene grown by chemical vapour deposition (CVD) directly onto copper (Cu) foil. The total thickness of the resulting battery was ∼50 μm. Such an ultrathin battery showed the highest energy density of 10 W h L−1 and the highest power density of 300 W L−1. It also shows excellent cyclic stability and sustains a discharge current density of 100 μA cm−2 over 100 cycles, maintaining energy capacity over 0.02 mA h cm−2.