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Abstract In this article, some new results as regards complete convergence for weighted sums ∑ i = 1 n a n i X i $\sum_{i=1}^{n}a_{ni}X_{i}$ of random variables satisfying the Rosenthal type inequality are established under some mild conditions. These results extend the corresponding theorems of Deng et al. (Filomat 28(3):509-522, 2014) and Gan and Chen (Acta Math. Sci. 28(2):269-281, 2008).