  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 to
constrain cosmological models. Though, the absolute magnitude of GRBs is still
unknown, the slopes of GRBs correlations can be used as a useful constraint to
dark energy in a completely cosmological model independent way. In this paper,
we follow Wang's model-independent distance measurement method and calculate
their values by using 109 GRBs events via the so-called Amati relation. Then,
we use the obtained model-independent distances to constrain $\Lambda$CDM model
as an example.
