This study aimed to fabricate composites with high thermal conductivity using diglycidyl ether of bisphenol-A (DGEBA), incorporating carbon fiber cloth (CFC) and graphene as reinforcing agents. Notably, the dispersion of graphene within the DGEBA matrix was enhanced through surface modification via a silane coupling agent. The effects of CFC and graphene addition on the impact strength, thermal conductivity, and morphology of the composites were examined. The experimental results showed that the incorporation of 6 wt% CFC resulted in a substantial (16-fold) increase in impact strength. Furthermore, the introduction of 6 wt% CFCs along with 20 wt% graphene led to a remarkable enhancement in thermal conductivity to 5.7 W/(m K), which was approximately 22 and 4 times higher than the intrinsic thermal conductivities of pristine DGEBA and the CFC/DGEBA composite, respectively. The increased impact strength is ascribed to the incorporation of CFC and silane-modified graphene. Additionally, the gradual increase in thermal conductivity can be attributed to the enhanced interaction between the acidic silane-modified graphene and the basic epoxy–amine hardener within the system studied.