In order to realize the evaluation of electrical properties of materials in nanoscale orders, a method for the measurement of local conductivity was presented. A microwave atomic force microscope (M-AFM) probe in which microwave signals can propagate was fabricated. An open structure of a waveguide at the tip of the probe was introduced by focused ion beam (FIB) fabrication. The microwave measurement system consisted of the combination of a network analyzer working at 44.5 GHz and an AFM were used to measure the samples without contact. The amplitude and phase of the reflection coefficient of the microwave signal were measured to determine the electrical conductivity of non magnetic metals. The conductivity obtained by this method agrees with that measured by the high-frequency conductometry.