Abstract: A single－electron transistor(SET) can be used as a sensitive electrometer whose sensitivity is limi－ted by noise. Shot noise is the intrinsic noise which determines the limit of sensitivity of the SET. Since an RF SET works at a very high frequency, its 1/f noise can be eliminated and thus the limit of sensitivity can be reached. An LC resonant circut is used to increase the characteristic impedance of the microwave system to couple with the output impedance of the SET, and so the sensitivity of the RF SET electrometer is improved.