Abstract: In this paper, by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent (NSD) random arrays and truncated method, we investigate the complete f-moment convergence of NSD random variables. We establish and improve a general result on the complete f-moment convergence for Sung's type randomly weighted sums of NSD random variables under some general assumptions. As an application, we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.