The thermal contact resistance (TCR) is one of the important components in the cryogenic systems. Especially, cryogenic measurement devices using a cryocooler can be affected by TCR because the systems have to consist of several metal components in contact with each other for heat transferring to the specimen without cryogen. Therefore, accurate measurement and understanding of TCR is necessary for the design of cryogenic measurement device using a cryocooler. The TCR occurs at the interface between metals and it can be affected by variable factors, such as roughness of metal surface, contact area and contact pressure. In this study, we designed TCR measurement system at various temperatures using a cryocooler as a heat sink and used steady state method to measure the TCR between metals. The copper is selected as a specimen in the experiment because it is widely used as a heat transfer medium in the cryogenic measurement devices. The TCR between Cu and Cu is measured for various temperatures and contact pressures. The effect of the interfacial materials on the TCR is also investigated.