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As so far, the redshift of Gamma-ray bursts (GRBs) can extend to $z\sim 8$which makes it as a complementary probe of dark energy to supernova Ia (SN Ia).However, the calibration of GRBs is still a big challenge when they are used toconstrain cosmological models. Though, the absolute magnitude of GRBs is stillunknown, the slopes of GRBs correlations can be used as a useful constraint todark energy in a completely cosmological model independent way. In this paper,we follow Wang's model-independent distance measurement method and calculatetheir values by using 109 GRBs events via the so-called Amati relation. Then,we use the obtained model-independent distances to constrain $\Lambda$CDM modelas an example.

Cosmological Model-independent Gamma-ray Bursts Calibration and its Cosmological Constraint to Dark Energy