Abstract: The edge-cloud computing systems are widely used to support various computation services. Aiming at the problem of task offloading and scheduling in edge-cloud computing environments, a stochastic task offloading problem in the edge-cloud computing system is considered. A greedy simulated annealing heuristic algorithm based online offloading framework(SAOF)is proposed for the problem under study, which periodically schedules and offloads tasks according to the required transmission delays and computation times. In consideration of the stochastic arrival of independent tasks and the heterogeneity of resources, SAOF assigns tasks to the appropriate destination (edge servers or cloud servers) dynamically and allocates computing resources to each task preemptively according to its latency-sensitivity. The goal is to minimize the sum of weighted response times of all the tasks. Testing instances are generated under the combination of various parameter settings for evaluation experiments. SAOF is compared with three excellent scheduling optimization algorithms(Selfish algorithm, Nearest algorithm and OnDisc algorithm). Experimental results indicate that SAOF can more effectively reduce the total weighted response time of all tasks.