In bulk power system， cascading failures initiated by branch outage events often lead to blackouts， it is necessary to carry out the event reliability analysis under emergency state. The influence of branch outages on system node voltage and line load is analyzed and a method can quickly calculate system node voltage and line load method under emergency state is introduced. The safety margin indices of node voltage and line load are also introduced. The reliability evaluation algorithm using state pruning by margin of safety is proposed. The margin of safety indices is applied to get the key states in all system fault states. Reliability indices are calculated by analyzing these key states. Some samples demonstrate its effectiveness and the computational complications of reliability analysis can be reduced.