With the rapid growth in electronic device performance, there has been an increasing demand for thermally conductive polymer composites to handle the thermal management issue, thus contributing to the great importance to develop the graphene framework, which is evaluated as the most promising reinforcements for enhancing the thermal conductivity of polymer. Vacuum filtration is a common method to fabricate graphene framework, whereas, it is available to prepare a framework with centimeter-scale thickness by filtrating the graphene-water dispersion, due to the fact of sample cracking caused by the mismatch of surface tension between graphene and water. In this work, a surfactant-assisted strategy was proposed by adjusting the surface tension of the water close to that of graphene first, then performing a conventional filtration process, to fabricate graphene framework. As a result, a thick graphene framework (thickness: 3 cm) was successfully prepared, and after embedding into epoxy, the framework endows the composite (13.6 wt％) with a high in-plane thermal conductivities of 12.4 W/mK, which is equivalent to≈64 times higher than that of neat epoxy. Our method is simple and compatible with the conventional filtration process, suggesting great potential for the mass-production of graphene framework to meet the practical application requirements.