The cloud computing and microsensor technology has greatly changed environmental monitoring, but it is difficult for cloud-computing based monitoring system to meet the computation demand of smaller monitoring granularity and increasing monitoring applications. As a novel computing paradigm, edge computing deals with this problem by deploying resource on edge network. However, the particularity of environmental monitoring applications is ignored by most previous studies. In this paper, we proposed a resource allocation algorithm and a task scheduling strategy to reduce the average completion latency of environmental monitoring application, when considering the characteristic of environmental monitoring system and dependency among task. Simulations are conducted, and the results show that compared with the traditional algorithms. With considering the emergency task, the proposed methods decrease the average completion latency by 21.6% in the best scenario.