  In this paper, we investigate the existence of the asymptotically almost
automorphic solution of the following type of abstract nonlinear
integro-dynamic equation \begin{eqnarray*} y^{\Delta}(s)
&=&Ay(s)+\mathcal{F}\left(s,y(s),\int\limits_{t_0}^{s}{\mathcal{H}(s,\tau,y(\tau))}\Delta\tau\right),~
s\in\mathbb{T}^k, y(0)&=&y_0 \end{eqnarray*} in the Banach space of continuous
function on a time scale $\mathbb{T}$. We apply the Krasnoselskii fixed point
theorem to show the existence of an almost automorphic solution of the above
dynamic equation.
