A new contingency screening and ranking method is proposed. Firstly， a load margin threshold is defined. The continuation power flow method is applied to compute the operating conditions under this load margin， at this operating point， the optimal multiplier algorithm is used to sequentially solve the outage power flow under all contingencies. Most of the contingencies， which have power flow solutions， are screened from the contingencies list as secure contingencies， and the other contingencies are considered as insecure contingencies. Secondly， at the base operating state， the optimal multiplier algorithm is used to solve the outage power flow of the insecure contingencies again. If the outage power flow has a solution， the contingencies are considered as critical contingencies and ranked by the load margin with the continuation power flow method; if it has no solution， the contingencies are unstable and can be ranked with the minimum costs of load shedding， which is obtained by successive linear programming method to make power flow equation solvable， and with the corrective control sensitivity information included in the mismatch of the least square solution. Case studies on New England 10-machine 39-bus show that the proposed method can be fast， reliable and comprehensive to achieve contingency screening and ranking for voltage stability analysis.