Possible indirect detection of neutralino, through its γ-ray annihilation product, by the forthcoming GLAST satellite from our galactic halo, M31, M87 and the dwarf galaxies Draco and Sagittarius is studied. γ-ray fluxes are evaluated for two representative energy thresholds, 0.1 GeV and 1.0 GeV, at which the spatial resolution of GLAST varies considerably. Apart from dwarfs, which are described either by a modified Plummer profile or by a tidally-truncated King profile, fluxes are compared for halos with central cusps and cores. It is demonstrated that substructures, irrespective of their profiles, enhance the γ-ray emission only marginally. The expected γ-ray intensity above 1 GeV at high galactic latitudes is consistent with the residual emission derived from EGRET data if the density profile has a central core and mχ ≤ 50 GeV, whereas for a central cusp only a substantial enhancement would explain the observations. From M31, the flux can be detected above 0.1 GeV and 1.0 GeV by GLAST only if mχ ≤ 300 GeV and if the density profile has a central cusp, case in which a significant boost in the γ-ray emission is produced by the central black hole. For Sagittarius, the flux above 0.1 GeV is detectable by GLAST provided the neutralino mass is below 50 GeV. From M87 and Draco the fluxes are always below the sensitivity limit of GLAST.