Steering nonlocality is the fundamental property of quantum mechanics, which has been widely demonstrated in some systems with qubits. Recently, theoretical works have shown that the high-dimensional (HD) steering effect exhibits novel and important features, such as noise suppression, which appear promising for potential application in quantum information processing (QIP). However, experimental observation of these HD properties remains a great challenge to date. In this work, we demonstrate the HD steering effect by encoding with orbital angular momentum photons for the first time. More importantly, we have quantitatively certified the noise-suppression phenomenon in the HD steering effect by introducing a tunable isotropic noise. We believe our results represent a significant advance of the nonlocal steering study and have direct benefits for QIP applications with superior capacity and reliability.