Metal Oxide Surge Arresters (MOSA) degrade in service under the working voltage, on-line measurement of the resistive current of MOSA is an effective method for judging the status of MOSA. In general, the measurement principle of the known detector doesn't consider the effect of the stray capacitance. In this paper based on a known non-liner v-i r mathematical model of the metal oxide valve element, a model of a MOSA including 7 metal oxide valve elements with stray capacitance to the ground is constructed. Through carrying out EMTP, the voltage and current characteristic of the MOSA is simulated. The simulation result shows the presence of stray capacitance leads to a non-uniform voltage distribution and the different phase shift of the voltage of the different MO valve element comparing with the applied voltage, the current wave shape distortion of the capacitance of the MO valve element. Based on the simulation result and adopting the known measurement method, measurement error will be produced