Model checking is a formal method to verify the system satisfies an expected property or not. Trere are two significant advantages of it, one is that it is fully automatic and the other is that if the system doesn't satisfy the checked property, it will generate an counterexamples which can help to fix errors in the system. The main purpose of this paper is to generate this counterexamples efficiently and intuitively. In order to generate the counterexamples efficiently and graphically display the operating processes of the system running alongside the concrete counterexamples, a system CCGS has been developed. Experimental results have shown that CCGS delivers an expected performance, and can help to improve the correctness and safety of the checked systems.