The static task list scheduling problems in distributed heterogeneous computing environment of Internet of things was studied, and a list scheduling algorithm named Heterogeneous Dynamic Priority Task Scheduling (HDPTS) was proposed, which can dynamically change scheduling sequence based on the strategy of the earliest completion time. Concerning that the exsiting list scheduling algorithms can not accurately determine the scheduling order before scheduling, on the basis of Improved Heterogeneous Earliest Finish Time (IHEFT) algorithm, a dynamic priority scheduling policy was added to it. When precursor tasks of a node completed scheduling, the scheduling priority of this node should be changed. Scheduling priority of task was calculated on the basis of choosing the maximum value between the latest completion time of all immediate predecessor tasks and the maximum available time of all the resources. At the same time, some other factors were also considered, including the influence to the subsequent tasks of the tasks assigned to the resource, the resource load, the calculated value of uplink weight and the influence to the exit tasks. All these considerations make the priority calculation be more reasonable, so as to dynamically change the task scheduling sequence reasonably according to the task allocation situation. By a randomly generated example test, the results show that the scheduling length of HDPTS reduced by 14.29% compared with IHEFT, HEFT (Heterogeneous Earliest Finish Time); the test results on a large number of randomly generated Directed Acyclic Graph (DAG) with specific structure prove that HDPTS is more effective than IHEFT, HEFT and LDCP (Longest Dynamic Critic Path) algorithms.