This paper investigates an energy-efficient hybrid flowshop scheduling problem with the consideration of machines with different energy usage ratios, sequence-dependent setups, and machine-to-machine transportation operations. To minimize the makespan and total energy consumption simultaneously, a mixed-integer linear programming (MILP) model is developed. To solve this problem, a three-stage multiobjective approach based on decomposition (TMOA/D) is suggested, in which each solution is bound with a main weight vector and a set of its neighbors. Accordingly, a variable direction strategy is developed to ensure each solution along its main direction is thoroughly exploited and can jump to the neighboring directions using a proximity principle. To ensure an active schedule of arranging jobs to machines, a two-level solution representation is employed. In the first phase, each solution attempts to improve itself along its current weight vector through a developed neighborhood-based local search. In the second phase, the promising solutions are selected through the technique for order preference by similarity to an ideal solution. Then, they attempt to update themselves with a proposed global replacement strategy via incorporation with their closing solutions. In the third phase, a solution conducts a large perturbation when it goes through all its assigned weight vectors. Extensive experiments are conducted to test the performance of TMOA/D, and the results demonstrate that TMOA/D has a very competitive performance.