A black-start decision support system is an important component of a smart grid. Up to now， research work on the decision-making of black-start strategies is mainly focused on individual decision-making methods， and no research work is reported on group decision-making ones. In practice， black-start decision-making is usually made by several decision makers， such as power dispatchers/domain experts， rather than by an individual one. Hence， it appears necessary to investigate the application of the group decision-making method to the development of optimal black-start strategies. Given this background， a group eigenvalue method is presented for the black-start decision-making. The positive eigenvectors associated with the maximal positive eigenvalue can be obtained with the application of the Perron-Frobenius theorem， and then the integrated evaluating value of the ideal black-start decision-making expert can be attained. The power method in the numerical algebra is employed to deal with the optimization problem associated with the group black-start decision-making. Finally， a numerical example is served for demonstrating the reasonableness and effectiveness of the developed method. It is demonstrated by case studies that the inherent shortcoming of the individual decision-making methods in evaluating black-start strategies could be overcome at least to some extent.