Abstract : We study the origin of the extragalactic diffuse gamma-ray background using the data from the Fermi telescope. To estimate the background level, we count photons at high Galactic latitudes |b| > 60°. Subtracting photons associated with known sources and the residual cosmic-ray and Galactic diffuse backgrounds, we estimate the extragalactic gamma-ray background (EGB) flux. We find that the spectrum of EGB in the very high energy band above 30 GeV follows the stacked spectrum of BL Lac objects. Large Area Telescope data reveal the positive (1 + z) k , 1 < k < 4 cosmological evolution of the BL Lac source population consistent with that of their parent population, Fanaroff-Riley type I radio galaxies. We show that EGB at E > 30 GeV could be completely explained by emission from unresolved BL Lac objects if k ~= 3.