  Gamma-ray bursts (GRBs) are one of the candidates of ultra-high-energy
(around 10^18.5 eV) cosmic-ray (UHECR) sources. We investigate high-energy
cosmic-ray acceleration including heavy nuclei in GRBs by using Geant 4, and
discuss its various implications, taking both of high-luminosity (HL) and
low-luminosity (LL) GRBs into account. This is because LL GRBs may also make a
significant contribution to the observed UHECR flux if they form a distinct
population. We show that not only protons but also heavier nuclei can be
accelerated up to ultra-high energies in the internal, (external) reverse and
forward shock models. We also show that the condition for ultra-high-energy
heavy nuclei such as iron to survive is almost the same as that for about TeV
gamma-rays to escape from the source and for high-energy neutrinos not to be
much produced. The multi-messenger astronomy by neutrino and GeV-TeV gamma-ray
telescopes such as IceCube and KM3Net, GLAST and MAGIC will be important to see
whether GRBs can be accelerators of ultra-high-energy heavy nuclei. We also
demonstrate expected spectra of high-energy neutrinos and gamma rays, and
discuss their detectabilities. In addition, we discuss implictaions of the
GRB-UHECR hypothesis. We point out, since the number densities of HL-GRBs and
LL-GRBs are quite different, its detemination by UHECR observations is also
important.
