We propose a strategy for active control of second harmonic generation (SHG) in a plasmonic Fano structure by electrically doping its underlying monolayer graphene. A detailed theoretical model for the proposed scheme is developed and numerical simulations are carried out to demonstrate the operation. Specifically, we show that a merely 30 meV change in graphene Fermi level can result in 45 times increase in SHG peak intensity, accompanied by a resonance wavelength shift spanning 220 nm. Further analysis uncovers that such tunability in SHG arises from the Fermi-level-modulated graphene permittivity, the real and imaginary parts of which dominate the resonance wavelength and the intensity of SHG, respectively.