This paper represents the design of the ground resistance measuring system insensitive to the noise in the earth. Generally, conventional ground resistance measuring instruments may fail to give a precise values for ground resistance under the situations where there is a high ground potential produced by unbalanced power system currents, haromonic currents and noise etc. To make up the defect of conventional ground resistance measuring instruments, in this paper the ground resistance measuring system using high-performance L-C resonant filter and digital signal processor is designed and the insentivity of the designed ground resistance measuring system for noise in the earth is verified by field test on power service and off power service.