As a low dimensional crystal, graphene attracts great attention as heat dissipation material due to its unique thermal transfer property exceeding the limit of bulk graphite. In this contribution, flexible graphene-carbon fiber composite paper is fabricated by depositing graphene oxide into the carbon fiber precursor followed by carbonization. In this full-carbon architecture, scaffold of one-dimensional carbon fiber is employed as the structural component to reinforce the mechanical strength, while the hierarchically arranged two-dimensional graphene in the framework provides a convenient pathway for in-plane acoustic phonon transmission. The as-obtained hierarchical carbon/carbon composite paper possesses ultra-high in-plane thermal conductivity of 977 W m(-1) K-1 and favorable tensile strength of 15.3 MPa. The combined mechanical and thermal performances make the material highly desirable as lateral heat spreader for next-generation commercial portable electronics.