Let {$X_n$, $n{geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=sum^n_{i=1}X_i$. In the paper, we get the precise results of H$acute{a}$jek-R$acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.