The paper presents results of a double polarization experiment to extract an asymmetry of the π − -meson photoproduction on a tensor-polarized deuteron by a linearly polarized photon. The energy of photons lies in the range (300–700) MeV. The measurements were performed on the internal tensor-polarized deuterium target in the VEPP-3 electron-positron storage ring for the electron beam energy equal to 2 GeV. In the experiment, two protons and a scattered electron were detected in coincidence. The results of the measurement are compared with theoretical predictions made in the framework of impulse approximation, taking into account the πN and NN-rescattering in the final state.