Fermi satellite released fairly accurate measurement of extragalactic gamma-ray background (EGB) from 100 MeV to 820GeV, which dramatically improve our understanding of the high energy gamma-ray background. But for TeV band, space detector is too small to help, and we must rely on ground based gamma-ray telescopes such as imaging atmospheric Cherenkov telescopes (IACTs). Until now, the extragalactic TeV gamma-ray background has not been well investigated. In this paper, we calculate the lower bound of extragalactic TeV gamma-ray background radiation by using the energy spectrum of low state of 61TeV sources, including 53 blazars, 6 radio galaxies, and 2 starburst galaxies, respectively. Our results show that blazars is the main contributor of the extragalactic TeV gamma-ray background, especially for Mrk 501 and Mrk 421, whose contribution at 0.5--4.5TeV is about 58%. And the contribution above 4.5TeV are mainly from the sources H 1426+428, 1ES 1959+650 and 1ES 0229+200, and their energy spectrum distribution has been extended to more than 10TeV. Finally, we calculate the contribution of blazars, radio galaxies, and starburst galaxies, respectively. Similar calculation is used to subclass of blazars and sources with different redshifts.