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We calibrated the peak energy–peak luminosity relation of gamma‐ray bursts (GRBs; the so‐called Yonetoku relation) using 33 events with redshift  z  &lt; 1.62 without assuming any cosmological models. The luminosity distances to GRBs are estimated from those of large numbers of Type Ia supernovae with  z  &lt; 1.755. This calibrated Yonetoku relation can be used as a new cosmic distance ladder towards higher redshifts. We determined the luminosity distances of 30 GRBs in 1.8 &lt;  z  &lt; 5.6 using the calibrated relation, and plotted the likelihood contour in the  (Ω m , Ω Λ )  plane. We obtained  (Ω m , Ω Λ ) = (0.37 +0.14  −0.11 , 0.63 +0.11  −0.14 )  for a flat universe. Because our method is free from the circularity problem, we can say that our universe in 1.8 &lt;  z  &lt; 5.6 is compatible with the so‐called concordance cosmological model derived for  z  &lt; 1.8. This suggests that the time variation of the dark energy is small or zero up to  z ∼ 6.

Gamma‐ray bursts in 1.8 < z < 5.6 suggest that the time variation of the dark energy is small