A bulk polycrystalline sample of YBa 2 Cu 3 O 7−δ (δ ≈ 0.1) has been irradiated by γ-rays with 60 Co source. Non-monotonic behavior of T c (defined as the temperature at which normal resistance is halved) with increasing irradiation dose Φ (up to about 220 MR) is observed: T c decreases at low doses (Φ ≤ 50 MR) from initial value (≈ 93 K) by about 2 K and then rises, forming minimum. At highest doses (Φ ≥ 120 MR) T c goes down again. The temperature width, δT c , of resistive transition increases rather sharp with dose below 75 MR and somewhat drops at higher dose. We believe that this effect is revealed for the first time at γ-irradiation of high-T c superconductor. The cross sections for the displacement of lattice atoms in YBCO by γ-rays due to the Compton process were calculated, and possible dpa values were estimated. The results obtained are discussed taking into account that sample studied is granular superconductor and, hence, the observed variations of superconducting properties should be connected primarily with the influence of γ-rays on intergrain Josephson coupling.