An increasing number of high-performance networks provision dedicated channels through circuit-switching or MPLS/GMPLS tunneling techniques to support large data transfer. The link bandwidths of these networks are typically shared by multiple users through advance scheduling and reservation. The sheer volume of data transfer across such networks in a national or international scope requires a significant amount of energy on a daily basis. However, most existing bandwidth scheduling algorithms only concern traditional objectives such as data transfer time minimization, and very limited efforts have been devoted to energy efficiency in high-performance networks. In this paper, we adopt a practical power model and formulate an advance instant bandwidth scheduling problem to minimize energy consumption under a data transfer deadline constraint. We design a polynomial-time optimal solution to this problem and provide a rigorous correctness proof. The performance superiority of the proposed solution in terms of energy saving is illustrated by extensive results based on both simulated and real-life networks in comparison with existing methods.