In order to avoid ignoring the serious faults in the screening and ranking which results in large-scale blackout of power grid, a new contingency screening and ranking method is proposed. It is based on solving the dynamic security domains, and can calculate dynamic security region of power system by analytic method to calculate the instability degrees. The instability degree of the fault is the indicator of contingency screening to quickly select the severe faults to form contingency screening set. Dynamic security region of power system can be calculated by BP neural network in contingency ranking to get probabilistic insecurity index. The probabilistic insecurity index of the faults is the indicator of contingency ranking to accurately rank. Case studies on New England 10-machine 39-bus system show that the proposed method can realize the contingency screening and ranking quickly, fully and accurately. Meanwhile, case studies on New England 4-machine 11-bus system show that the calculation of dynamic security region about BP neural network is feasible, the error is 0.0608, which can meet the requirements.