The rapid improvement in the running speed, transmission efficiency, and power density of miniaturized devices means that multifunctional flexible composites with excellent thermal management capability and high electromagnetic interference (EMI) shielding performance are urgently required. Here, inspired by the fibrous pathways of the human nervous system, a “core–sheath” fibers structured strategy was proposed to prepare thermoplastic polyurethane/polydopamine/carbon nanotube (TPU/PDA/CNT) composites film with thermal management capability and EMI shielding performance. Firstly, TPU@PDA@CNT fibers with CNT shell were prepared by a facile polydopamine-assisted coating on electrospun TPU fibers. Subsequently, TPU/PDA/CNT composites with three-dimensional (3D) fibrous CNT “tracks” are obtained by a hot-pressing process, where CNTs distributed on adjacent fibers are compactly contacted. The fabricated TPU/PDA/CNT composites exhibit a high in-plane thermal conductivity (TC) of 9.6 W/(m·K) at low CNT loading of 7.6 wt.%. In addition, it also presents excellent mechanical properties and excellent EMI shielding effectiveness of 48.3 dB as well as multi-source driven thermal management capabilities. Hence, this study provides a simple yet scalable technique to prepare composites with advanced thermal management and EMI shielding performance to develop new-generation wireless communication technologies and portable intelligent electronic devices.