Naocrystalline (nc) material shows lower thermal conductivity than its coarse grain counterpart, which restricts its engineering applications. In order to study the effects of grain size and grain boundary on the thermal conductivity of nc material, nc copper is prepared by the high pressure sintering method. The pure nc Cu powder is used as the starting material, and the high pressure sintering experiment is carried out under a DS614 MN cubic press. Prior to the high pressure sintering experiment, the Cu powders are first pre-compressed into cylinders, then they are compressed under 5 GPa at temperatures ranging from 700 to 900 ℃ for 30 min. The grain size and micro-structural characteristics are investigated by the scanning electron microscope (SEM) and X-ray diffraction (XRD). The results show that the sintered Cu bulk material can achieve nearly full densification with a relative density of 99.98% and the grain growth of the Cu particles is effectively inhibited. The thermal conductivity measurement is performed by NETZSCH LFA-427 at 300 K and 45% RH. The test results show that the thermal conductivity of nc copper is lower than that of its coarse grain counterpart, and the thermal conductivity increases with grain size increasing. For example, as the grain size increases from 390 to 715 nm, the corresponding thermal conductivity increases from 200.63 to 233.37 Wm-1K-1, which are 53.4% and 60.6% of the thermal conductivity of the coarse grain copper, respectively. For a better understanding of the effects of grain boundary and size on the thermal conductivity of nc material, a simple modified model, with special emphasis on the contributions of electron and phonon conduction, is presented by incorporating the concept of the Kapitza resistance into an effective medium approach. The theoretical calculations are in good agreement with our experimental results. The combination of experimental results and theoretical calculations concludes that the thermal conductivity of nc material is weakened mainly by two factors: the grain boundary-electron (phonon) scattering on the grain boundary and the electron (phonon)-electron (phonon) scattering in the grain interior. That is to say, the thermal resistance of nc material can be divided into two parts: one is the intragranular thermal resistance from the grain, the other is the intergranular thermal resistance from the grain boundaries. As is well known, when the grain size decreases to a nano-range, the volume fraction of the grain boundary presents a sharp increase, and the intergranular thermal resistance from the grain boundaries becomes more important.