To address the challenges posed by the dynamism, high latency, and resource scarcity in integrated air-space-ground hybrid edge cloud environments on task completion times and node load, we designed a task scheduling system for scenarios involving the transmission and processing of interdependent tasks. This system integrates a graph neural network with attention mechanism and deep reinforcement learning. Specifically, we employ a graph encoder to extract features from DAG tasks and resources. Task scheduling solutions for dynamic environments are then generated using attention mechanism-equipped graph decoder, which are subsequently optimized based on performance metrics through the use of an Advantage Actor-Critic algorithm. Experimental results indicate that this algorithm performs well in terms of completion time and node load balance across tasks with different workflow structures, demonstrating its adaptability to highly dynamic edge cloud environments.