Abstract: Edge computing is commonly applied in emerging fields such as the Internet of things, the Internet of vehicles, and online games. Edge computing provides low-latency computing services for terminal devices by deploying computing resources at network edges. How to offload tasks to balance execution time and communication time and how to schedule tasks with different deadlines with the objective of minimizing the total tardiness are challenging problems. In this paper, a task offloading and scheduling framework is proposed for the heterogeneous edge computing. There are five components included in the framework: sequencing edge network nodes, sequencing offloaded task, task offloading strategies, task scheduling and the solution improvement. Multiple task offloading and task scheduling strategies are designed and embedded. ANOVA (multi-factor analysis of variance) is used to calibrate the algorithmic components and parameters over a large number of random instances. The algorithm with the best component combination is obtained. Based on the EdgeCloudSim simulation platform, several variants of the proposed algorithm are compared with the proposed algorithm from the perspectives of the number of edge nodes, the number of tasks, the distribution of tasks, and the interval of deadlines. Experimental results show that the proposed algorithm outperforms the other comparisons in all cases.