  An important concern in the application of gamma-ray bursts (GRBs) to
cosmology is that the calibration of GRB luminosity/energy relations depends on
the cosmological model, due to the lack of a sufficient low-redshift GRB
sample. In this paper, we present a new method to calibrate GRB relations in a
cosmology-independent way. Since objects at the same redshift should have the
same luminosity distance and since the distance moduli of Type Ia supernovae
(SNe Ia) obtained directly from observations are completely cosmology
independent, we obtain the distance modulus of a GRB at a given redshift by
interpolating from the Hubble diagram of SNe Ia. Then we calibrate seven GRB
relations without assuming a particular cosmological model and construct a GRB
Hubble diagram to constrain cosmological parameters. From the 42 GRBs at
$1.4<z\le6.6$, we obtain $\Omega_{\rm M}=0.25_{-0.05}^{+0.04}$,
$\Omega_{\Lambda}=0.75_{-0.04}^{+0.05}$ for the flat $\Lambda$CDM model, and
for the dark energy model with a constant equation of state
$w_0=-1.05_{-0.40}^{+0.27}$, which is consistent with the concordance model in
a 1-$\sigma$ confidence region.
