Heterodyne instruments have recently attained quantum-limited low-noise performance, particularly in radio astronomy, but it is difficult to develop large heterodyne arrays such as a modern radio camera using cryogenic sensitive detectors based on microwave kinetic inductance detectors, transition edge sensors, etc. In the realization of the heterodyne array, the reduction of power dissipation for semiconductor-based amplifiers remains a major challenge. Alternatively, superconducting parametric amplifiers still seem to have several barriers to application, especially in terms of operating temperature. Here, we show a novel concept of microwave amplification based on up and down frequency-conversion processes using quasiparticle superconductor-insulator-superconductor (SIS) tunnel junctions. We demonstrate positive gain using a proof-of-concept test module, which operates with a power dissipation of several μW at a bath temperature of 4 K. The performance of the module suggests great potential for application in large arrays.