  We study the $\gamma$-ray emission from the pulsar magnetosphere based on
outer gap models, and the TeV radiation from pulsar wind nebulae (PWNe) through
inverse Compton scattering using a one-zone model. We showed previously that
GeV radiation from the magnetosphere of mature pulsars with ages of $\sim
10^5-10^6$ years old can contribute to the high latitude unidentified EGRET
sources. We carry out Monte Carlo simulations of $\gamma$-ray pulsars in the
Galaxy and the Gould Belt, assuming the pulsar birth rate, initial position,
proper motion velocity, period, and magnetic field distribution and evolution
based on observational statistics. We select from the simulation a sample of
mature pulsars in the Galactic plane ($|b|\leq 5^\circ$) and in the high
latitude ($|b|> 5^\circ$) which could be detected by EGRET. The TeV flux from
the pulsar wind nebulae of our simulated sample through the inverse Compton
scattering by relativistic electrons on the microwave cosmic background and
synchrotron seed photons are calculated. The predicted fluxes are consistent
with the present observational constraints. We suggest that strong EGRET
sources can be potential TeV source candidates for present and future
ground-based TeV telescopes.
