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Identifying and preferentially reinforcing critical lines for skeleton-network of power systems is significant in improving the secure and stable operation of power systems under extreme weather conditions. Under this background, in this paper, six indexes are first presented for identifying critical lines for skeleton-network with the power elements’ parameters and the impact of extreme weather conditions, the network topology and the operation state of power systems considered. Then, the modified Vise Kriterijumska Optimizacija I Kompromisno Resenje in Serbian (VIKOR) method, in which the synthetic weights of indexes determined by the combination weighting method are adopted, is utilized to identify the importance degrees of lines in a given power system. Both the overall performance and the outstanding individual performance of lines are considered, which is beneficial for the critical lines identification for skeleton-network. Finally, the proposed multi-indexes and methods are applied to part of the actual Guangdong power system in China. The numerical results are compared with those obtained by single-attribute and multi-attribute evaluation methods and other evaluation methods. [ABSTRACT FROM AUTHOR]