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The compatible-invariant subset of deterministic finite automata (DFA) is investigated to solve the problem of subset stabilization under the frameworks of semi-tensor product (STP) of matrices.The concepts of compatible-invariant subset and largest compatible-invariant subset are introduced inductively for Moore-type DFA,and a necessary condition for the existence of largest compatible-invariant subset is given.Meanwhile,by using the STP of matrices,a compatible feasible event matrix is defined with respect to the largest compatible-invariant subset.Based on the concept of compatible feasible event matrix,an algorithm to calculate the largest compatible-invariant subset contained in a given subset is proposed.Finally,an illustrative example is given to validate the results.