Carbon nanotubes (CNTs)/epoxy composites are composed of CNTs, epoxy resin, and the interphase between them. The micro-morphology of the interphase has a significant influence on the macro-properties of composites, which is mainly attributed to the difference in the interaction between CNTs and epoxy resin. However, a systematic research on the interaction between CNTs and epoxy resin on composite properties is still insufficient. In this paper, the surface properties of three types of functionalized CNTs, the adhesion forces between the typical functional groups and epoxy groups, as well as the curing characteristics and the thermal properties of the CNTs/epoxy composites were investigated by using experimental methods like surface energy analysis, atomic force microscopy, and differential scanning calorimetry. This paper performed direct measurements on the interaction between CNTs with functional groups and epoxy resin. Moreover, it provided several experimental evidences for the mechanism of interfacial interaction affecting thermal properties of CNTs/epoxy composites. It indicated that it is conducive to form covalent bonds at the CNTs/epoxy composite interface when there is a strong interaction between CNTs and epoxy resin, and the thermal property could be improved finally.