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Let {Y i ; −∞ < i < ∞} be a doubly infinite sequence of identically distributed and ρ *-mixing random variables with zero means and finite variances and {a i ; −∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of { P n k=1 P ∞ i=−∞ a i+k Y i /n 1/p ; n ≥ 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 ρ *-mixing case.

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