We consider the system of two parallel sheets of graphene which are moving with relative parallel velocity v ⃗ and calculate the Casimir energy by using the scattering approach. We analyze in detail the normal (perpendicular to the planes) Casimir force for two systems—graphene/graphene and ideal metal/graphene. In the non-relativistic case v ≪ v F , the relative correction to the Casimir energy ( E v − E 0 ) / E 0 is proportional to the ( v / c ) 2 (the maximum value is 0.0033 for the gapeless case and v = v F ) for the first system, and it is zero up to the Fermi velocity v = v F for system ideal metal/graphene.