We formed a GRB cosmology project in Japan, and promote the observational cosmology with Gamma‐ray bursts (GRBs). In this paper, we introduce recent result of our project with the spectral Epeak‐Luminosity relations. We show the Hubble diagram up to the redshift of z = 8.2, and the confidence contour of the dark energy Λ) and the dark matter m) beyond z>2 beyond the current range measured by the Type Ia supernovae. After that, we investigate the origin of data dispersion of the Epeak‐brightness relations, and suggest a possible improvement of their accuracy.

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