In this paper, we shall prove some strong laws of large numbers(SLLN's) for weighted sums of set-valued random variables in the sense of Hausdorff metric $d_H$ for which the basic space being Rademacher type $p~ (1\leq p\leq 2)$ Banach space. We partially follow the results of classical SLLN's for ${\X}$-valued random variables in \cite{AdRoTa}, extending it to more general set-valued case.