Abstract: Low-frequency radio observations on the lunar surface have great potential for scientific discovery and are expected to reveal the secrets of the dark age and cosmic dawn of the Universe. This paper proposes a new design for low-frequency radio lunar observation. The non-Foster matching circuit is used to significantly reduce the physical size of the antenna, making it light and easy to deploy on the moon. First, an electrically small membrane antenna which is light, wide temperature range, malleable, foldable, simple to deploy, and with good omnidirectionality is designed, gain is less than 1.92 dB in 4-8 MHz and half-beam width is greater than 83°. Then, a non-Foster matching circuit is employed to improve impedance performance, the reactance of the antenna is optimized from about -985.3 Ω to -16.5 Ω, and the noise power level is less than -150 dBm in most frequency range. Finally, The feasibility of the design is preliminarily confirmed by impedance and noise measurement.