Abstract: Along with the wide application of UML modeling in software development, the automatic generation of test cases based on state diagram gradually becomes the major research direction of specification-based testing. By analyzing some existing methods, this paper proposes a new generation algorithm based on function minimization technique, in which the depth-first-search and memorized-search strategy is utilized to obtain test cases. Experiment shows that the present method can achieve a higher coverage rate of path via fewer test cases.