An algorithm for constructing the simplified DFA(Deterministic Finite Automaton) is introduced,which is equivalent to a given regular expression. The first step constructs an NFA(Nondeterministic Finite Automaton) equivalent to the regular expression, where the operation for constructing finite automata with ε-moves is omitted. Then the simplified DFA equivalent to the NFA is constructed by using state transition trees. The algorithm bas been realized by computer programming, and for any input regular expression, a simplified DFA equivalent to the regular expression is produced. The algorithm can be applied in the design and analysis of the system with discrete inputs and outputs.