  Using a simple accelerating model and an assumption that $\gamma$-rays
originate from $p-p$ collisions for a $\pi^0$ model, we investigate
$\gamma$-ray sources like V407 Cygni in symbiotic stars. The upper limit of
their occurrence rate in the Galaxy is between 0.5 and 5 yr$^{-1}$, indicating
that they may be an important source of the high-energy $\gamma$-rays. The
maximum energies of the accelerated protons mainly distribute around $10^{11}$
eV, and barely reach $10^{15}$ eV. The novae occurring in D-type SSs with ONe
WDs and long orbital periods are good candidates for $\gamma$-ray sources. Due
to a short orbital period which results in a short acceleration duration, the
nova occurring in symbiotic star RS Oph can not produce the $\gamma$-ray
emission like that in V407 Cygni.
