All kinds of differential equations as mathematical models have been built up due to different practical problems，so the problem of studying the existence of various solutions has attracted the attention of mathematical scholars at home and abroad. The problem on the existence and uniqueness of asymptotically almost automorphic mild solutions for a class of neutral differential equations with delay are researched by using Banach compression mapping principle，related theorems of almost automorphic type functions and the exponential dichotomy of convolution family in this paper. Asymptotically almost automorphic mild solutions are more general than almost automorphic mild solutions，so the research of this paper will make the scope of application on this kind of differential equations more extensive.