Optical second harmonic generation (SHG) is studied from multilayer graphene films in the presence of dc electric current flowing in the sample plane. Graphene layers are manufactured by the chemical vapor deposition technique and deposited on an oxidized Si(001) substrate. SHG intensity from the graphene layer is found to be negligible in the absence of the dc current, while it increases dramatically with the application of the electric current. The current-induced change of the SHG intensity from graphene/SiO2/Si(001) rises linearly with the current amplitude and changes its sign under the reversal of the current direction to the opposite. The observed effect is explained in terms of the interference of second harmonic radiation reflected from the Si surface and that induced by the dc current in multilayer graphene.