Heterostructures based on parallel graphene layers separated by thin dielectrics are among the main components of the novel electronic devices: optical and plasmon modulators, transistors and photodetectors. Thin dielectric layers ( 3 nm) enable the resonant tunneling of electrons between the graphene sheets. In the report, it is shown that a double graphene layer tunneling structure can play a role of a gain medium for plasmons, simiar to the quantum cascade lasers based on superlattices. Plasmon gain coefficient is shown to exceed the loss associated with the interband and intraband transitions in graphene. The frequency dependence of plasmon gain coefficient exhibits a resonance attributed to the strong interaction between electrons with parallel momenta in graphene layers.