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In recent years, edge computing, as an important pillar for future networks, has been developed rapidly. Task offloading is a key part of edge computing that can provide computing resources for resource-constrained devices to run computing-intensive applications, accelerate computing speed and save energy. An efficient and feasible task offloading scheme can not only greatly improve the quality of experience (QoE) but also provide strong support and assistance for 5G/B5G networks, the industrial Internet of Things (IIoT), computing networks and so on. To achieve these goals, this paper proposes an adaptive edge task offloading scheme assisted by service deployment (SD-AETO) focusing on the optimization of the energy utilization ratio (EUR) and the processing latency. In the pre-implementation stage of the SD-AETO scheme, a service deployment scheme is invoked to assist with task offloading considering each service's popularity. The optimal service deployment scheme is obtained by using the approximate deployment graph (AD-graph). Furthermore, a task scheduling and queue offloading design procedure is proposed to complete the SD-AETO scheme based on the task priority. The task priority is generated by the corresponding service popularity and task offloading direction. Finally, we analyze our SD-AETO scheme and compare it with related approaches, and the results show that our scheme has a higher edge offloading rate and lower resource consumption for massive task scenarios in the edge network.