Most research on the short-circuit current contributed by wind turbine driven doubly-fed induction generator(DFIG) focuses on the non-grid-connected DFIG and grid-connected DFIG with the short-circuit point located at the generator's terminal. When the DFIG is connected to a distribution network, the short-circuit current of DFIG may be affected by the characteristics of the distribution network, the location of the short-circuit point and other factors. First, based on the Park model of induction motor, a detailed mathematical derivation for the transient characteristics of DFIG in the external fault is conducted and analyzed. The composition of the short-circuit current of DFIG and an approximate expression of the short-circuit current are proposed. Then, the effect factors to short-circuit current of DFIG are analyzed. Finally, the simulation shows the correctness of the analysis.