SummaryWith the rapid development of the Internet of Things (IoT), fog computing has emerged as a complementary solution to address the issues faced in cloud computing. However, it is a challenging issue to ensure both of the high Quality of Service (QoS) and low cost for different requests when dealing with computing resources. In this article, we propose a new approach on adaptive cost‐efficient and QoS‐aware application placement for fog computing called DATSS. Specifically, this approach consists of a QoS state driven strategy and a credibility rating mechanism. The algorithm divides the QoS into three different states by calculating the QoS violation rate and adaptively selects the best scheduling strategy. Then evaluates the stability of the node based on the task history, and prioritize the task on the node with a higher rating. Performance results show that the cost, delay and energy consumption of the proposed algorithm can be reduced by 20.9%, 15.7%, and 12.6% respectively compared with other algorithms at most. The proposed algorithm can effectively improve cost efficiency and stability under QoS constraints in fog computing environments.