The emergence of network function virtualization (NFV) technology enables network services instantiated as service function chains (SFCs) to share the underlying network, alleviating the rigidity of traditional network architectures. However, the large number of service requests in the network brings new challenges to multi-domain SFC orchestration. For one thing, the privacy of the intra-domain resource information and internal policies of the network makes multi-domain SFC orchestration more complicated. For another, multi-domain SFC orchestration requires the determination of the optimal set of candidate orchestration domains. Nevertheless, previous studies rarely considered the inter-domain load balance, which negatively affected the service acceptance rate. In addition, the orchestration of service requests across network domains places more stringent requirements on the cost and response time of the service. To address the above challenges, this study proposes a construction method for domain-level graphs to meet the privacy requirement of multi-domain networks. Then, a calculation method for domain weight based on the inter-domain load balance is proposed to select SFC orchestration domains. Finally, the study proposes an orchestration algorithm considering the cost and responses time requirements of multi-domain networks. The experimental results show that the proposed algorithm effectively trades off the average service cost and the acceptance rate and also optimizes the average service response time.