  The population of $\gamma$-ray emitting millisecond pulsars (MSPs) is studied
by using Monte-Carlo techniques. We simulate the Galactic distributions of the
MSPs, and apply the outer gap model for the $\gamma$-ray emission from each
simulated MSP. We take into account the dependence of the observed $\gamma$-ray
flux on the viewing angle and inclination angle, which is the angle between the
rotation axis and the magnetic axis, respectively. Using the sensitivity of the
six-month long observation of the $Fermi$ telescope and radio sensitivities of
existing pulsar surveys, 9-13 radio-selected and 22-35 $\gamma$-ray-selected
pulsars are detected within our simulation. The statistical properties of the
simulated population are consistent with the $Fermi$ observations. Scaling the
observed sensitivity $\propto \sqrt{T}$, where $T$ is the length of observation
time, the present model predicts that over the 5-year mission $Fermi$ would
detect 15-22 radio-selected $\gamma$-ray MSPs, and 95-152 $\gamma$-ray-selected
MSPs. Our simulation also predicts that about 100 (or 200-300) $\gamma$-ray
MSPs with a flux larger $F\ge 10^{-11}~\mathrm{erg/cm^2 s}$ (or $5\times
10^{-12}~\mathrm{erg/cm^2 s}$) irradiate the Earth. With the present
sensitivities of the radio surveys, most of them are categorized as
$\gamma$-ray-selected pulsars, indicating that most of the $\gamma$-ray MSPs
have been missed by the present $Fermi$ observations. We argue that the
Galactic $Fermi$ unidentified sources located at high latitudes should be
dominated by MSPs, whereas the sources in the galactic plane are dominated by
radio-quiet canonical pulsars.
