Let ${(X_{ni}|1{leq}i{leq}n,;n{geq}1)}$ be an array of rowwise negatively associated random variables. In this paper we discuss $n^{{alpha}p-2}h(n)max_{1{leq}k{leq}n}|{sum}_{i=1}^kX_{ni}|/n^{alpha}{ ightarrow}0$ completely as $n{ ightarrow}{infty}$ under not necessarily identically distributed with suitable conditions for ${alpha}$>1/2, 0<p<2, ${alpha}p{geq}1$ and a slowly varying function h(x)>0 as $x{ ightarrow}{infty}$. In addition, we obtain the complete convergence of moving average process based on negative association random variables which extends the result of Zhang (1996).