Nuclear security is an important part of national security. To deal with the lack of quantitative methodologies in the current researches, the GMCR（graph model for conflict resolution） was adjusted and applied to games analysis for nuclear crisis. Firstly, the analysis framework, the related definitions and the matrix representation approaches were proposed. Secondly, the conflict model was calibrated based on the history background of the Sino-Soviet nuclear crisis in 1969, and the evolution of game state was unveiled by using matrix analysis algorithms. Thirdly, two parameters of conflict model were introduced, namely game policy and military capability, and the sensitivity analysis for their influence to stability results was researched. Fourthly, coalition analysis methodologies were utilized to identify the potential alliances of decision makers and its impact on national relation evolution. Finally, relevant conclusions and decision suggestions of nuclear security were summarized based on the analysis results of the conflict model. Results show that the GMCR is suitable for investigating nuclear crisis and the strategy matching with military capability play a key role in game evolution.