Tree-related failure caused by large-scale power flow transferring is one of the most important causes of power grid catastrophic accident. Predicting the flashover time and probability after the later tripping is an important subject to prevent system blackouts. Considering dominant vegetation growth, circumstance and power flow transferring, quantitative depicting method for the influencing factors and prediction method of line fault probability and time are proposed. Combining the randomness of influencing factors and power flow, an approximate linearization method is used to determine line heat time factor. With the help of probability density function of line contacting tree, line contacting tree time and probability is predicted. Two cases simulation results show that the contacting time and probability mainly depend on line final steady state power and circumstance factors. When the line power flow is changing tempestuously, the proposed method can predict the tree-related fault time and probability in time. These results can provide reasonable decision-making for power system operators to prevent power system blackout.