Abstract: To address the challenge of jointly optimizing makespan and system energy consumption in multi-objective flexible job shop scheduling problems, an end-to-end scheduling method based on graph neural networks and conditional multi-objective proximal policy optimization (CMO-PPO) is proposed. Firstly, the scheduling process is formulated as a multi-objective Markov decision process, in which makespan and total energy consumption are represented as vectors. Subsequently, the scheduling system is modeled as a heterogeneous graph composed of operation nodes and machine nodes, and structured state features are encoded by a graph neural network. On this basis, a multi-objective PPO framework with vector rewards and vector value functions is constructed. A delayed scalarization fusion mechanism is introduced at the advantage estimation level to ensure stable policy updates, while preference-conditioned policies are employed to enhance the generalization capability of the model under different objective trade-offs. Experimental results demonstrate that, compared with NSGA-II, FNSGA, and NRainbow, the proposed method is capable of obtaining Pareto solution sets with relatively high quality and broader coverage in most benchmark instances, thereby exhibiting good multi-objective optimization performance.