We propose and substantiate the concept of terahertz (THz) laser enabled by the resonant electron radiative transitions between graphene layers (GLs) in double-GL structures. We estimate the THz gain for TM-mode exhibiting very low Drude absorption in GLs and show that the gain can exceed the losses in metal-metal waveguides at the low end of the THz range. The spectrum of the emitted photons can be tuned by the applied voltage. A weak temperature dependence of the THz gain promotes an effective operation at room temperature.The gapless energy spectrum of graphene layers (GLs) [1] enables the creation of different terahertz (THz) devices utilizing the interband transition. In particular, the interband population inversion and the pertinent negativity of the dynamic conductivity in GLs [2,3] due to the optical or injection pumping can be used in GL-based THz lasers [4][5][6][7][8][9]. First experimental results on the THz emission from optically excited GLs [10] (see also review paper [11] and references therein) instill confidence in the realization of such lasers. One of the obstacles, limiting the achievement of the negative dynamic conductivity in the range of a few THz, is the reabsorption of the photons with the in-plane polarization emitted at the interband transitions due to the intraband transitions (the Drude absorption). Similar situation takes place in the quantum cascade lasers (QCLs) based on multiple quantum well (MQW) structures [12]. However, in the case of the photon polarization perpendicular to the QW plane the intraband (intrasubband) absorption can be much weaker than that following from the semi-classical Drude formula [13].In this paper, we propose a device structure based on a double-GL structure shown in Fig. 1 (upper panel) with the injection of electrons to one n-doped GL and to another p-doped GL, which can be used for lasing of THz photons with the electric field perpendicular to the GL plane due to the tunneling inter-GL radiative processes. The structure band diagram under the applied bias voltage and tunneling transitions assisted with the emission of photons with the energy ω ∼ ∆, where ∆ is the energy distance (gap) between the Dirac points in GLs, are demonstrated in Fig. 1 (lower panel). These transitions take place from the conduction band of the GL with 2DEG to the empty conduction band of GL with 2DHG. The transition from the filled valence band the former GL to the empty portion of the valence band of the latter GL also contribute to the emission of photons with ω ∼ ∆. The structure comprises two GLs with the side contact at one of the GL edges. This double-GL structure plays the role of the laser active region. The opposite edge of GL is isolated from another contact. A narrow tunneling-transparent barrier separates GLs (its thickness d is about few nanometers). The applied bias voltage V provides the formation of the two-dimensional electron and hole gases (2DEG and 2DHG) in the upper and lower GLs, respectively owing to the injection from the side contacts, so that the ...