A NaI(Tl) detector array called DALI2 (Detector Array for Low Intensity radiation 2) has been constructed for in-beam γ-ray spectroscopy experiments with fast radioactive isotope (RI) beams. It consists typically of 186 NaI(Tl) scintillators covering polar angles from ∼15 • to ∼160 • with an average angular resolution of 6 • in full width at half maximum. Its high granularity (good angular resolution) enables Doppler-shift corrections that result in, for example, 10% energy resolution and 20% full-energy photopeak efficiency for 1-MeV γ rays emitted from fast-moving nuclei (velocities of v/c ≃ 0.6). DALI2 has been employed successfully in numerous experiments using fast RI beams with velocities of v/c = 0.3 − 0.6 provided by the RIKEN RI Beam Factory.