Current open issues regarding cloud computing include the support for nontrivial Quality of Service-related Service Level Objectives (SLOs) and reducing the energy footprint of data centers. One strategy that can contribute to both is the integration of accelerators as specialized resources within the cloud system. In particular, Field Programmable Gate Arrays (FPGAs) exhibit an excellent performance/energy consumption ratio that can be harnessed to achieve these goals. In this paper, a multilevel cloud scheduling framework is described, and several FPGA-aware node level scheduling strategies (applied at the hypervisor level) are explored and analyzed. These strategies are based on the use of a multiobjective metric aimed at providing Quality of Service (QoS) support. Results show how the proposed FPGA-aware scheduling policies increment the number of users requests serviced with their SLOs fulfilled while energy consumption is minimized. In particular, evaluation results of a use case based on a multimedia application show that the proposal can save more than 20% of the total energy compared with other baseline algorithms while a higher percentage of Service Level Agreement (SLA) is fulfilled.