A design for a GaN/AlGaN optically pumped terahertz laser emitting at 34 μm (ΔE~36 meV) is presented. This laser uses a simple three-level scheme where the depopulation of the lower laser level is achieved via resonant longitudinal-optical-phonon emission. The quasibound energies and associated wave functions are calculated with the intrinsic electric field induced by the piezoelectric and the spontaneous polarizations. The structures based on a double quantum well were simulated and the output characteristics extracted using a fully self-consistent rate equation model with all relevant scattering processes included. Both electron-longitudinal-optical phonon and electron-acoustic-phonon interactions were taken into account. The carrier distribution in subbands was assumed to be Fermi-Dirac-like, with electron temperature equal to the lattice temperature, but with different Fermi levels for each subband. A population inversion of 12% for a pumping flux Φ=1027 cm-2 s-1 at room temperature was calculated for the optimized structure. By comparing the calculated modal gain and estimated waveguide and mirror losses the feasibility of laser action up to room temperature is predicted.