As none of the currently used restoration methods of the black-start stage for power systems has retained the restoration security margin while intent only on the maximization of profitability indices，serious security risks may result in the restoration process.At the same time，the preference factors of decision makers and the actual situation of system restoration cannot be well synthesized in the existing black-start decision-making methods.An extended black-start multi-objective optimization method considering both power support and restoration security margin is proposed.The optimization goals are designed to maximize the total weighted power generation output of the black-start system and voltage stability margin，while maintaining bus voltage at a satisfactory level.A multi-objective optimization model is developed for the black-start schemes by comprehensive consideration of all the constraints of the unit start-up time and system operation.The fast and elitist non-dominated sorting genetic algorithm（NSGA-Ⅱ）and the Dijkstra algorithm are employed to solve the Pareto-optimal solutions of the extended black-start schemes.By using the Vague set multi-attribute decision-making method based on fuzzy entropy weight and considering the preference factors of decision makers and objective information of decision matrix，the most satisfactory solution is identified.The effectiveness of the proposed method is validated by optimization results on the New England 10-unit 39-bus power system and the Southern power system of Hebei Province.