Cloud computing environments facilitate applications by providing virtualised resources through the network and serve the clients by the pay‐as‐you‐go mechanism. It is based on the rapid development of the network. Normally, economic cost is the most important factor of providing cloud services. However, under some special conditions, the objectives may change. In this scenario, it is impractical to reset the scheduling mechanism only for an occasional incident. So an adaptive scheduling mechanism is needed to address the issues of scheduling under different conditions. To the best of our knowledge, no works have well solved this problem. In this paper, we convert the problem to a multi‐objective scheduling problem with varying objective weights and propose a two‐phase algorithm, which is called adaptive priority‐based workflow scheduling (DRAWS) algorithm. The algorithm will self regulate the priorities of tasks to adapt to different objectives. In the experimental part, simulation environments are set up and three classic workflows are used to evaluate the performance. Four comparing algorithms of resource sensitive scheduling algorithm, Best Fit‐millions of instructions per second, Best Fit‐random‐access memory and Best Fit‐Bandwidth are used to evaluate the performance of DRAWS. It is demonstrated that each phase of our algorithm would optimise the scheduling. Furthermore, we obtain the conclusion that DRAWS algorithm shows superior than the comparing algorithms. Copyright © 2015 John Wiley & Sons, Ltd.