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Human-robot interaction (HRI) is an important area of robotics research. The speech interaction is a key issue of natural communication between user and robots. This paper proposes a speech interaction system based on finite state machine (FSM) and each step of the interaction is defined to be a state of the FSM. The control flow of the conversation is described by the dynamic behavioral model of speech interaction system based on FSM. The logical expression of inter behaviors and the operability of the conversation are convenient for the users. The user application interface and design process of conversation based on extensible markup language (XML) are introduced. Experimental results indicated that our speech interaction system could achieve over 93% accuracy in 60-dBA noise.