With the development of network functions virtualization and software defined networking, the service function chain (SFC) orchestration issue is a big challenge for high reliability and low latency services. At present, many studies propose solutions in terms of physical node mapping or link mapping for SFC. In this paper, we consider parallel transmission by dividing the SFC request flow into multiple subflows. To solve the problem of orchestrating parallel SFC under the premise of being able to meet the delay requirements of delay-sensitive classes of services, we divide the problem into two parts: virtual network functions mapped to physical servers and virtual links mapped to physical links. In the first part, we find suitable physical nodes for deployment by the simulated annealing algorithm. In the second part, we construct the link mapping problem as a multi-objective optimization problem. We solve this multi-objective optimization problem by quantum genetic algorithm. Finally, the mapping scheme for parallel SFC is generated. We have conducted comparative analyses of the algorithms through simulation experiments. The results show that the method proposed in this paper can effectively improve the orchestration efficiency of parallel SFC. The algorithm we build can not only minimize the resource consumption and routing energy consumption but also meet the delay requirements well. Therefore, this paper has high practical significance in diverse delay-sensitive service applications and provides a solution for future multipath parallel SFC orchestration.