We propose a low-noise and low-power-consumption microwave amplifier using superconductor-insulator-superconductor (SIS) mixers as quasi-particle frequency up- and down-converters pumped by a Josephson array oscillator in the millimeter-wave band. A proof-of-concept study of an amplifier with two W-band waveguide mixers using Nb/Al-AlOx/Nb junctions in a cascade connection demonstrated an average gain of 6 dB and a noise temperature of 12 K from nearly DC to 5 GHz. We also designed and fabricated a Josephson array oscillator at 100 GHz, which consisted of 31 overdamped Josephson junctions placed at each half-wavelength in an Nb microstrip line. The estimated output power of the oscillator was 0.2 μW at 100 GHz, which can be increased by increasing the number of the oscillator junctions. These results suggest that the proposed SIS mixer-based amplifier is suitable for on-chip integrated circuits to be implemented in large-scale multipixel SIS receivers and quantum computers.