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This paper presents the design and fabrication of a reflex klystron oscillator based on a carbon nanotube (CNT) cold-cathode. An X-band klystron oscillator structure is assembled with a CNT cold-cathode electron gun with an electrostatic focusing, a re-entrant cavity as anode, and a repeller. The electron gun adopts a convex CNT film emitter as the cathode. A re-entrant cavity resonating at 8.376 GHz is fabricated. The study mainly focuses on the returning electron beam in the klystron oscillator structure. The experimental results of variations of the anode current and returning electron beam amplitude with repeller voltage are presented. It is demonstrated that a higher extracting voltage of the cold-cathode has an important influence on the returning electron beam. To decelerate electron velocity from the extracting voltage, increasing negative focusing voltage and focusing electrode height in the electron gun can improve the returning electron beam characteristics.