AI-based network function virtualization (NFV) is an emerging technique that separates network control functionality from dedicated hardware middleboxes and is virtualized to reduce capital and operational costs. With the advances of NFV and AI-based software-defined networks, dynamic network service demands can be flexibly and effectively accomplished by connecting multiple virtual network functions (VNFs) running on virtual machines. However, such promising technology also introduces several new research challenges. Due to resource constraints, service providers may have to deploy different service function chains (SFCs) to share the same physical resources. Such sharing inevitably forces the scheduling of the SFCs and resources, which consumes computational time and introduces problems associated with reducing the response delay. In this paper, we address this challenge by developing two dynamic priority methods for queuing AI-based VNFs/services to improve the user experience. We account for both transmission and processing delays in our proposed algorithms and achieve a new processing order (scheduler) for VNFs to minimize the overall scheduling delay. The simulation results indicate that the proposed scheme can promote the performance of AI-based VNFs/services to meet strict latency requirements.