Edge servers provide low-latency, high-performance services for mobile intelligent applications. However, due to significant fluctuations in the load on edge servers over time, many edge servers remain idle during periods of low load, and their computational resources are not fully utilized. In contrast to the underutilization of edge servers, computing resources in cloud computing clusters remain relatively scarce for deep learning training tasks as artificial intelligence becomes more widely applied in daily life. Existing cluster scheduling strategies fail to efficiently utilize idle computing resources outside of cloud computing clusters. Effectively utilizing these idle resources can alleviate the resource constraints in cloud computing clusters, thus enabling more deadline-sensitive deep learning training tasks to be completed before their deadlines. To address this issue, this study proposes a cluster scheduling strategy for deadline-sensitive deep learning training tasks, which coordinates the scheduling of cloud computing resources and idle edge computing resources. This strategy fully leverages the performance characteristics of different deep learning tasks and the availability of idle edge server devices, allowing more deadline-sensitive tasks to be completed on time. Simulation results demonstrate that the cloud-edge collaborative scheduling method outperforms other benchmark methods in improving the deadline satisfaction ratio and effectively utilizes idle edge server devices.