Since a class of specific differential equations called cellular neural networks with delays have been established，the discussion on existence and uniqueness of all kinds of solutions for this class of equation becomeimportant study contents，especially the study on almost periodic type solutions. In order to study asymptotically almost functions，applications on a class of cellular neural networks with varying delays，the existence anduniqueness of asymptotically almost periodic solutions on this class of cellular neural networks are discussed by using Banach fixed point theorem and some knowledge on exponential dichotomy，combining with the research ofalmost periodic solutions on this class of cellular neural networks in some literature，and it is proved that this class of cellular neural networks has unique asymptotically almost periodic solution under some sufficient conditions.