With the widespreader use of precision devices and semiconductors in daily life and production process, power users have higher requirements for voltage quality.Power quality problems such as sag caused by faults cannot be ignored. To quantify the risk of voltage sags under short-circuit faults, Monte Carlo simulations are usually required, but the amount of calculation is large.In order to accelerate the complete probability sag assessment of distribution network, this paper proposes a fast algorithm based on equivalent calculation and analytical fitting.In this paper, the equivalent algorithm of combined load model is applied to calculate the fault power flow, and the fitting function of the analytical form is solved according to the calculation result. Then the concepts of voltage critical threshold and minimum tolerance threshold are introduced by considering the difference of the degree of influence of the different dip interregional. Finally the assessment is realized by integral and weighted summation.Experiments were carried out on the IEEE33 distribution network system, the difference between the result of applying the algorithm and the one of the Monte Carlo method is extremely little. The former has obvious advantages in time consumption.