It is very important to predict the coupling between the cavity and the high power input source in the coupler design. In this paper, a time domain method is used to calculate the extal quality factor Qext for the BEPC Ⅱ superconducting cavity. A comparison between simulation results and experimental results is presented. The results of simulation and measurement of Qext have a good agreement within an error of 10%.The geometry parameters related with Qext are also studied.