<p>In this paper, the authors consider a wave-plate transmission system on Riemannian manifold with boundary controls on the plate equation. This model arises from the noise control and is extended to the broader context of the Riemannian manifold. By employing the semigroup method, the authors obtain the well-posedness of the system. Subsequently, under certain geometric conditions, the authors establish a polynomial energy decay estimate of type <i>t</i>⁻¹ by using the geometric multiplier method in which the conclusion proposed by Guo and Yao (2006) plays a crucial role in the obtained proof. It effectively addresses the challenge posed by curvature on the Riemannian manifold. Moreover, by employing the higher-order energy method, the authors overcome the technical difficulties caused by higher-order terms in boundary controls, which generalizes the results in the literature.</p>