Dynamic scheduling problems have been receiving increasing attention in recent years due to their practical implications. To realize real-time and the intelligent decision-making of dynamic scheduling, we studied dynamic permutation flowshop scheduling problem (PFSP) with new job arrival using deep reinforcement learning (DRL). A system architecture for solving dynamic PFSP using DRL is proposed, and the mathematical model to minimize total tardiness cost is established. Additionally, the intelligent scheduling system based on DRL is modeled, with state features, actions, and reward designed. Moreover, the advantage actor-critic (A2C) algorithm is adapted to train the scheduling agent. The learning curve indicates that the scheduling agent learned to generate better solutions efficiently during training. Extensive experiments are carried out to compare the A2C-based scheduling agent with every single action, other DRL algorithms, and meta-heuristics. The results show the well performance of the A2C-based scheduling agent considering solution quality, CPU times, and generalization. Notably, the trained agent generates a scheduling action only in 2.16 ms on average, which is almost instantaneous and can be used for real-time scheduling. Our work can help to build a self-learning, real-time optimizing, and intelligent decision-making scheduling system.