Motivated by the scheduling challenges of high-performance computing in the information industry, this paper investigates a bi-objective energy-efficient flow-shop scheduling problem under time-of-use tariffs. To comprehensive consideration of practical factors, including release dates, due dates, task energy consumption and processor maintenance, a mixed-integer programming model is established, and an ϵ-constraint approach is adopted to convert the bi-objective model into several single-objective ones to achieve Pareto-optimal fronts. For better achieving the trade-off of energy consumption and customer satisfaction, total electricity cost and maximum lateness criteria are simultaneously introduced as minimizing objects. The superiority of the developed approach is demonstrated through experiments.