Abstract Gamma-ray bursts (GRBs) are the most luminous explosions in and can be detectable out to the edge of the universe. They have long been thought to be able to extend the Hubble diagram to very high redshifts. Several correlations between temporal or spectral properties and GRB luminosities have been proposed to make GRBs cosmological tools. However, those correlations cannot be properly standardized. In this paper, we select a long-GRB sample with X-ray plateau phases produced by electromagnetic dipole emissions from central newborn magnetars. A tight correlation is found between the plateau luminosity and the end time of the plateau in the X-ray afterglows out to the redshift z = 5.91. We standardize these long-GRB X-ray light curves to a universal behavior through this correlation, with a luminosity dispersion of 0.5 dex. The derived distance–redshift relation of GRBs is in agreement with the standard ΛCDM model both at low and high redshifts. The evidence for an accelerating universe from this GRB sample is 3 σ , which is the highest statistical significance from GRBs to date.