To investigate the device which is capable of generate and amplify a coherent electromagnetic radiation in the millimeter and submillimeter wavelength ranges is extremely important today. In the research under discussion the model of a plasma-beam superheterodyne free electron laser (SFEL) is the following. Plasma is located in the longitudinal focusing magnetic field with strength H0. Relativistic electron beam is injected into this plasma environment at an angle α with respect to the magnetic field strength vector. We chose a circularly polarized intense low-frequency electromagnetic wave as a pump. This wave propagates along the guiding magnetic field and in the opposite direction to the electron beam. Also we feed a weak high-frequency circularly polarized electromagnetic wave (signal wave) into the system. The direction of the wave signal may be different, so the wave number can either positive or negative. The parametric resonance between the signal wave and the pump wave results in excitation of a space-charge wave (SCW).