  Inspired by increase of population of $\gamma$-ray emitting pulsars by the
$Fermi$ telescope, we perform a population study for $\gamma$-ray emitting
canonical pulsars. We use a Monte-Carlo technique to simulate the Galactic
population of neutron stars and the radio pulsars. For each simulated neutron
star, we consider the $\gamma$-ray emission from the outer gap accelerator in
the magnetosphere. In our outer gap model, we apply the gap closure mechanism
proposed by Takata et al., in which both photon-photon pair-creation and
magnetic pair-creation processes are considered. Simulating the sensitivities
of previous major radio surveys, our simulation predicts that there are $\sim
18-23$ radio loud and $\sim 26-34$ $\gamma$-ray-selected $\gamma$-ray pulsars,
which can be detected with a $\gamma$-ray flux $F_{\gamma}\ge
10^{-10}~\mathrm{erg/cm^2 s}$. Applying the sensitivity of the six-month
observation of the $Fermi$ telescope, 40-61 radio-selected and 36-75
$\gamma$-ray selected pulsars are detected within our simulation. We show that
the distributions of various pulsar parameters for the simulated $\gamma$-ray
pulsars can be consistent with the observed distribution of the $\gamma$-ray
pulsars detected by the $Fermi$ telescope. We also predict that $\sim 64$
radio-loud and $\sim 340$ $\gamma$-ray-selected pulsars irradiate the Earth
with a flux $F_{\gamma}\ge 10^{-11}~\mathrm{erg/cm^2 s}$, and most of those
$\gamma$-ray pulsars are distributing with a distance more than 1~kpc and a
flux $F_{\gamma}\sim 10^{-11}~\mathrm{erg/cm^2 s}$. The ration between the
radio-selected and $\gamma$-ray-selected pulsars depend on the sensitivity of
the radio surveys. We also discuss the Galactic distribution of the
unidentified $Fermi$ sources and the canonical $\gamma$-ray pulsars.

High Energy Astrophysical Phenomena