In this paper, we investigate the existence and uniqueness ofa piecewise asymptotically almost periodic mild solution tononautonomous neutral Volterra integro-differential equations withimpulsive effects in Banach space. The working tools are based onthe Krasnoselskii's fixed point theorem and semigroup theory. Inorder to illustrate our main results, we study the piecewiseasymptotically almost periodic solution of the impulsive partialdifferential equations with Dirichlet conditions.