The open-shop scheduling problem is a typical NP-hard problem. Most of the existing research assumes that the processing time of a procedure is fixed. However， in real-world production scenarios， the processing time can be controlled by adjusting the processing power. At the same time， optimizing the two conflicting objectives of completion time and energy consumption is significant for the high-efficiency and energy-saving open-shop production. Therefore， the Multi-objective Open-shop Scheduling Problem with Controllable Processing Time （MOOSPCPT） was studied， a mixed-integer programming model was constructed with the objectives of minimizing makespan and total extra energy consumption， and a Multi-objective Hybrid Evolutionary Algorithm （MOHEA） was proposed to solve MOOSPCPT. Several strategies were developed in the MOHEA： 1） the migration strategy and mutation strategy in the biogeographic-based optimization algorithm were improved for global search， which facilitated the diversity of the population effectively； 2） a self-adjusting variable neighborhood search strategy was designed based on the critical path， which enhanced the local search performance of the algorithm； 3） a processing time resetting operator was designed， which improved the search efficiency of the algorithm significantly. Simulation results show that the proposed strategies are effective in improving algorithm performance； MOHEA solves MOOSPCPT more effectively compared with Non-dominated Sorting Genetic Algorithm Ⅱ （NSGA-Ⅱ）， Non-dominated Sorting Genetic Algorithm Ⅲ （NSGA-Ⅲ） and Strength Pareto Evolutionary Algorithm 2 （SPEA2）.