The effects of various situations on friction torque in the first phase for repairing of 7075-T6 aluminum alloy by friction plug welding were analyzed,and the friction torque mathematical model in the first phase of frictional plug welding was established. The various conditions include welding feed speed,welding rotation speed,taper angle of the plug. The results showed that,the peak torque and elapsed time for peak torque to it were affected by welding feed speeds and welding rotation speeds. The peak torque decreased with increasing the welding rotation speed and it increased with increasing the welding feed speed,and the elapsed time for peak torque decreased with increasing the welding feed speed and the welding rotation speed. As the taper angle of the plug increased,the friction torque before the peak torque increased accordingly,but the peak torque and the elapsed time for peak torque hardly changed.