A mathematical model of high speed rotational arc sensor, which is used in gas metal arc welding (GMAW) of fillet joints, is developed. It is based on the mathematical model of GMA welding system and Halmoy's wire melting model. The variations of welding current, arc length and wire extension are simulated by using the developed model. It is shown that the simulation results of welding current, arc length and wire extension agree with the experimental results in fillet joints. Based on the mathematical model, the variation of arc length is bigger than that of wire extension. The deviation and direction of the welding gun can be detected by the difference between the left half-cycle current and the right half-cycle current during each torch rotational cycle. In addition, the end point of the fillet joint can be detected by the average current value in each torch rotational cycle. The mathematical model developed is helpful to the design and application of high speed rotational arc sensors.