  We investigate non-thermal emission from the Fermi bubbles on a hadronic
model. Cosmic-ray (CR) protons are accelerated at the forward shock of the
bubbles. They interact with the background gas in the Galactic halo and create
$\pi^0$-decay gamma-rays and secondary electrons through proton-proton
interaction. We follow the evolution of the CR protons and electrons by
calculating their distribution functions. We find that the spectrum and the
intensity profile of $\pi^0$-decay gamma-rays are consistent with observations.
We predict that the shock front is located far ahead of the gamma-ray boundary
of the Fermi bubbles. This naturally explains the fact that a clear temperature
jump of thermal gas was not discovered at the gamma-ray boundary in recent
Suzaku observations. We also consider re-acceleration of the background CRs in
the Galactic halo at the shock front. We find that it can significantly affect
the gamma-rays from the Fermi bubbles, unless the density of the background CRs
is $\lesssim 10$\% of that in the Galactic disk. We indicate that secondary
electrons alone cannot produce the observed radio emission from the Fermi
bubbles. However, the radio emission from the outermost region of the bubbles
can be explained, if electrons are directly accelerated at the shock front with
an efficiency of $\sim 0.1$\% of that of protons.
