Let {$Y_{ij}-{infty};<;i;<;{infty}$} be a doubly infinite sequence of identically distributed and ${ ho}^*$-mixing random variables with zero means and finite variances and {$a_{ij}-{infty};<;i;<;{infty}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {${sum}^n_{k=1};{sum}^{infty}_{i=-{infty}};a_{i+k}Y_i/n^{1/p}$; $n;{geq};1$} under some suitable conditions. We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), 191.197.] to the ${ ho}^*$-mixing case.