Network virtualization allows the coexistence of multiple virtual networks on a shared substrate network. A virtual network created by a service provider (SP) typically spans across multiple domains that may be managed by different infrastructure providers (InPs). The topology and resource information on each domain is confidential and kept private by the InP. However, a domain-level view is required to achieve quality of service (QoS)-aware VN mapping across multiple domains. In this paper, we present a framework for the QoS-aware VN mapping across multiple domains. In the framework, the VN mapping is accomplished by the mapping manager that is the broker between the SPs and the InPs. The mapping manager collects the mapping candidates for the VN request from the InPs, and then establishes the abstracted domain-level graph. Finally the candidates are selected on the domain-level graph with QoS consideration. We formulate the problem of candidate selection as an integer linear programming (ILP) and also present a heuristic algorithm to solve it. The simulation results show that our proposed framework can achieve low resource allocation cost and good QoS performance for the VN request.