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The minimum spanning tree (MST) model was applied to research the evolutionary relationships of tRNA gene sequences. The MSTs of tRNA gene sequences are constructed by the Prim's algorithm. The topology of the tRNA gene sequences-Ala, Leu, Met and Ser is discussed and shows the relationships among different kinds of tRNA sequences. The result of the MST shows they have the similar structure and behavior which reveals that the tRNA gene may have the fastest and optimized evolutionary path. The topology of MSTs exposes tRNA gene sequences has the homologous fractal structure and its network provides interesting information that the degree distribution becomes the power-law distribution.