Improving production efficiency and developing green catalytic systems are key issues for applying Heck coupling reactions in the chemical industry. In this study, an amidoxime-fiber-supported Pd catalyst is prepared from polyacrylonitrile fiber, hydroxylamine hydrochloride, and PdCl2. The morphology and structure of amidoxime-fiber-supported Pd are characterized by scanning electron microscopy, energy-dispersive spectroscopy, X-ray photoelectron spectrometer, X-ray diffraction, and inductively coupled plasma-optical emission spectrometer. A packed-bed flow reactor is designed and employed for catalysis of the Heck reaction of iodobenzene and styrene based on the amidoxime-fiber-supported Pd catalyst. The effects of reaction temperature, flow rate, cycle time, and reactant concentration on the conversion and yield are investigated. The results show that the optimal conditions for the continuous-flow single reactor are 70 °C, iodobenzene concentration of 30 mmol L−1 in a solution of N,N-dimethylformamide (100 mL) under continuous flow at a flow rate of 2 mL min−1. The catalyst showed good activity and stability after a continuous operation time of 50 h, with catalytic activity 2.21 times higher than that obtained with traditional batch reaction. Furthermore, we have established a new flow reaction system based on the numbering-up of reactors with a parallel connection. The catalytic efficiency of four parallel reactors is four times higher than that of a single reactor. Kinetic studies reveal that the reaction has low activation energy (8.8771 kJ mol−1), indicating that amidoxime-fiber-supported Pd has good catalytic activity. This research provides an alternative pathway for highly efficient Heck coupling in continuous flow.