In recent decades, the rapid development of nanoscience and nanotechnology has accelerated materials with high thermal conductivity, such as composite carbon nanomaterials, since heat removal has become a crucial issue. In this work polyacrilonitrile (PAN) incorporated with alteration of mass fraction (0.3 wt%, 0.62 wt%, 0.92 wt%, 2.74 wt%) of the multi-walled carbon nanotubes (MWCNTs) were used to fabricate composite fibers via electrospinning. The stabilizing and carbonization reactions of composite nanofibers are conducted in tube furnace at 280 degrees C and 1000 degrees C. The structural features of flexible composite carbon nanofiber papers were characterized under scanning electron microscopy (SEM), X-ray powder diffraction (XRD) and Raman spectroscopy. Special attention of composite carbon nanofiber papers is given to cross-plane thermal conductivity and in-plane thermal conductivity and were measured via Flash Line Analyzer. The results proved that flexible composite carbon nanofiber papers are promising heat sink radiator for a variety of applications including flexible optical and electronic devices.