  In this paper, we calibrate the Amati relation (the $E_{\rm p}$-${E}_{\rm
iso}$ correlation) of gamma-ray bursts (GRBs) in a cosmology-independent way.
By using Gaussian process to reconstruct the smoothed luminosity distance from
the Pantheon type Ia supernovae (SNe Ia) sample, we utilize the reconstructed
results to calibrate the $E_{\rm p}$-${E}_{\rm iso}$ correlation with the
Markov Chain Monte Carlo method and construct a Hubble diagram with the A220
GRB data, in which there are A118 GRB data with the higher qualities
appropriate for cosmological purposes. With 98 GRBs at $1.4<z\leq8.2$ in the
A118 sample and the observed Hubble data, we obtain $\Omega_{\rm
m}$=$0.346^{+0.048}_{-0.069}$, $h$=$0.677^{+0.029}_{-0.029}$ for the flat
$\Lambda$CDM model, and $\Omega_{\rm m}$=$0.314^{+0.072}_{-0.055}$,
$h$=$0.705^{+0.055}_{-0.069}$, $w$=$-1.23^{+0.33}_{-0.64}$ for the flat $w$CDM
model, which are consistent with those from fitting the coefficients of the
Amati relation and the cosmological parameters simultaneously.
