Aiming at the shortcomings of the existing weak link identification methods in the distribution network, a method for identifying weak links of the power grid based on off-grid load capacity was proposed, which considered the effect of the magnitude and duration of voltage sag on sensitive equipment. First, the magnitude and duration were divided into multiple intervals. Then, the analytical method was used to calculate the probability of the node voltage magnitude in each interval when the line failed; the probability density function of the duration distribution was fitted to calculate the probability of the voltage sag duration in each interval. From this, the probability of the magnitude and duration of node voltage sag in each interval was obtained when the line failed; that was the occurrence probability of voltage sag. Finally, based on the occurrence probability of voltage sag and the failure probability of sensitive equipment in each interval, the failure probability of sensitive equipment caused by line failure and the total off-grid load capacity of the power grid were calculated, and the off-grid load capacity was used as an indicator for identifying weak links of the power grid. Taking the IEEE-39 node system as an example for verification analysis and comparing it with other methods, the results showed the effectiveness of the proposed method.