We describe a new, in principle, layout of a graphene resonator—a differential resonator, which makes it possible to increase substantially its sensitivity to the mass deposited on it. The differential resonator consists of two parallel graphene films, which are fastened in insulating supports; the lower film is arranged over the conducting surface. The force coupling between the films is performed by the electrostatic field in the space between them. Several equilibrium positions are possible in such a mechanical system. Small free oscillations near the stable equilibrium position are considered. The field strength is selected so that the mechanical system of two graphene films would have two close eigenfrequencies. The free oscillations of such a system have the form of intrinsic frequencies of the system much lower that the partial frequency of each film. When depositing the particle on the upper film, the partial eigenfrequency of this film decreases. In this case, the characteristic envelope frequency also decreases, and a small variation in the partial eigenfrequency leads to considerable variation in the characteristic envelope frequency. This provides higher sensitivity to the mass of the revealed particle for the differential resonator compared with the resonator based on one film.