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Exponent stability is considered as a higher level of stability than asymptotic stability. To realize chaotic synchronization with better synchronization capability, a theory of exponent stability was introduced to the research of chaotic synchronization, and an approach of chaotic synchronization with exponent stability of the synchronization error system was discussed. On the premise that the states of the aim chaotic system were observable, an approach of exponent stability by nonlinear feedback control based on the bounded property of the tracks was proposed for the chaotic synchronization, which made the chaotic synchronization errors satisfy exponent stability, and realized the chaotic synchronization in according to exponent stability. That is to say, the capability of chaotic synchronization was improved, while the chaotic systems arrived at the chaotic synchronization. Theory analysis and simulation results had proved the feasibility and validity of the approach. When applied in the fields of chaotic secure communication and others, the prospect will be perfect.