The uniform exponential instability of

GC

(0

e

) -generalized evolution operator in Banach space is studied. Based on the definition of 

GC

(0

e

) -generalized evolution operator

the necessary and sufficient conditions for uniform exponential instability are obtained via mathematical analysis and operator theory. The results extend some well-known results in exponential stability theory. The research is theoretically important for studying the instability of generalized evolution operator.