The growing prevalence of edge computing and its more profound incorporation into cloud computing has given rise to the advent of the multi-center scenarios. This presents a significant challenge in the context of task scheduling. However, the existing task scheduling systems either designs for single cloud/edge center or several edge servers. Few systems support cross-center cloud-edge collaborative scheduling. In this work, we propose a secure cloud-edge collaborative task scheduling system that can generate scheduling plans across multiple data centers. The system supports time-sharing scheduling, multitask scheduling and task offloading between centers at the same time. It generates scheduling plans with the priority-based time-sharing policy, and adopts the deep-Q-network-based multitask policy and the dynamic task offloading policy. The experimental results indicate that the scheduling delay increases linearly with the number of concurrent submitted tasks. The scheduling delay is little affected by the number of data centers.