Flexible Job-shop scheduling, which is a traditional combinatorial optimization problem, becomes more crucial in intelligent manufacturing. However, traditional methods fail to capture the complex scheduling relationships, leading to suboptimal solutions. Therefore, this paper proposes a novel end-to-end deep reinforcement learning framework to address this issue. Specifically, our method extracts appropriate pairs of machines and operations from the disjunctive graph as a set of decision actions and dynamically updates it to reduce the complexity. Further, our method employs two interconnected graph attention modules for machines and operations to facilitate message passing. Each module utilizes a multi-head graph attention network, incorporating convolutional layers in each head to enhance the representation capability of the method. Experimental results on larger and diverse datasets demonstrate the superiority of the proposed method.