  The very hard $\gamma$-ray spectrum from distant blazars challenges the
traditional synchrotron self-Compton (SSC) model, which may indicate that there
is the contribution of an additional high-energy component beyond the SSC
emission. In this paper, we study the possible origin of the hard $\gamma$-ray
spectrum from distant blazars. We develop a model to explain the hard
$\gamma$-ray spectrum from blazar 1ES 1101-232. In the model, the optical and
X-ray radiation would come from the synchrotron radiation of primary electrons
and secondary pairs, the GeV emission would be produced by the SSC process,
however, the hard $\gamma$-ray spectrum would originate from the decay of
neutral pion produced through proton-photon interactions with the synchrotron
radiation photons within the jet. Our model can explain the observed SED of 1ES
1101-232 well, especially the very hard $\gamma$-ray spectrum. However, our
model requires the very large proton power to efficiently produce the
$\gamma$-ray through proton-photon interactions.
