  In this paper, we compile a \emph{Fermi} sample of the \emph{long} GRB
observations from 15 years of GBM catalogue with identified redshift, in which
the GOLD sample contains 123 long GRBs at $z\le5.6$ and the FULL sample
contains 151 long GRBs with redshifts at $z\le8.2$. The Amati relation (the
$E_{\rm p,i}$-$E_{\rm iso}$ correlation) are calibrated at $z<1.4$ by a
Gaussian Process from the latest observational Hubble data (OHD) with the
cosmic chronometers method so that GRBs at high-redshift $z\ge1.4$ can be used
to constrain cosmological models via the Markov chain Monte Carlo (MCMC)
method. From the cosmology-independent GRBs with the GOLD sample at $z\ge1.4$
and the Pantheon+ sample of type Ia supernovae (SNe Ia) at $0.01<z\leq2.3$, we
obtain $\Omega_{\rm m} = 0.354\pm0.018, H_0 = 73.05\pm0.2\,\rm{km/s/Mpc}$ for
the flat $\Lambda$CDM model; $w_0 = -1.22^{+0.18}_{-0.15}$ for the flat $w$CDM
model; and $w_{a} = -1.12^{+0.45}_{-0.83}$ for the flat
Chevallier-Polarski-Linder model at the 1$\sigma$ confidence level. Our results
with the GOLD and FULL sample are almost identical, which are more stringent
than the previous results with GRBs.
