The logistics industry has entered the era of highly information-based intelligent logistics. In order to save resource consumption and improve the cooperation efficiency between robots, a centralized computing mode has emerged in the application of warehousing robots, namely, logistics cloud robots. In order to improve the work efficiency of the logistics cloud robot, this paper designs a task resource scheduling model of the cloud logistics robot in the edge computing environment. The logistics cloud robot can improve the response efficiency by unloading some delay sensitive tasks to the edge server, and assign the delay insensitive tasks to the cloud computing center. Therefore, it is particularly important to reasonably allocate tasks to appropriate computing cells. The model combines graph convolution network and heuristic algorithm, and designs a joint scheduling strategy to unload requests to edge services and cloud servers reasonably, so as to maximize the use of computing resources. Based on the joint scheduling strategy, the optimal long-term scheduling decision is generated to reduce scheduling time and improve service quality. To evaluate the effectiveness of the model, we use heterogeneous earliest completion time (HEFT) and other algorithms as benchmarks to compare the performance of the model. In order to verify the authenticity of the scheduling scheme, we conducted simulation experiments on the EdgeCloudSim platform to verify the quality of service of task scheduling in different scenarios. The experimental results show that the proposed method is superior to most of the comparison methods and can better optimize the task scheduling efficiency of the logistics cloud robot.