  The theory of universal extra dimensions involves Kaluza-Klein (KK)
particles. The lightest KK particle (LKP) is one of the good candidates for
cold dark matter. Annihilation of LKP dark matter in the Galactic halo produces
high-energy gamma-rays. The gamma-ray spectrum shows a characteristic peak
structure around the LKP mass. This paper investigates the observability of
this peak structure by near-future detectors taking account of their energy
resolution, and calculates the expected energy spectrum of the gamma-ray
signal. Then, by using the HESS data, we set some constraints on the boost
factor, which is a product of the annihilation cross section relative to the
thermal one and an uncertain factor dependent on the substructure of the LKP
distribution in the Galactic halo, for each LKP mass. The resulting upper limit
on the boost factor is in the range from 1 to 30. The constraints can be
regarded as comparable with the results of previous work for gamma-ray and
electron-positron observation. However, the observational data for the TeV or
higher energy region are still limited, and the possible LKP signal is not
conclusive. Thus, we expect near-future missions with better sensitivity will
clarify whether the LKP dark matter should exist or not.
