  It is expected that specific globular clusters can contain up to a hundred of
millisecond pulsars. These pulsars can accelerate leptons at the shock waves
originated in collisions of the pulsar winds and/or inside the pulsar
magnetospheres. Energetic leptons diffuse gradually through the globular
cluster comptonizing stellar and microwave background radiation. We calculate
the GeV-TeV $\gamma$-ray spectra for different models of injection of leptons
and parameters of the globular clusters assuming reasonable, of the order of
1%, efficiency of energy conversion from the pulsar winds into the relativistic
leptons. It is concluded that leptons accelerated in the globular cluster cores
should produce well localized $\gamma$-ray sources which are concentric with
these globular clusters. The results are shown for four specific globular
clusters (47 Tuc, Ter 5, M13, and M15), in which significant population of
millisecond pulsars have been already discovered. We argue that the best
candidates, which might be potentially detected by the present Cherenkov
telescopes and the planned satellite telescopes (AGILE, GLAST), are 47 Tuc on
the southern hemisphere, and M13 on the northern hemisphere. We conclude that
detection (or non-detection) of GeV-TeV $\gamma$-ray emission from GCs by these
instruments put important constraints on the models of acceleration of leptons
by millisecond pulsars.
