Let $x, y \in {R}^{n}$, we say $x$ is ut-Toeplitz weak majorized by $y$ (written as $x\prec_ {uT}y$) if there exists an upper triangular substochastic Toeplitz matrix $A$ such that $x=Ay$. In this paper, we characterize all linear functions that strongly preserve $\prec_ {uT}$ on ${R}^n$.