We present the detection of a young brown dwarf companion DH Tau B associated with the classical T~Tauri star DH Tau. Near-infrared coronagraphic observations with CIAO on the Subaru Telescope have revealed DH Tau B with H=15 mag located at 2.3 (330 AU) away from the primary DH Tau A. Comparing its position with a Hubble Space Telescope archive image, we confirmed that DH Tau A and B share the common proper motion, suggesting that they are physically associated with each other. The near-infrared color of DH Tau B is consistent with those of young stellar objects. The near-infrared spectra of DH Tau B show deep water absorption bands, a strong KI absorption line, and a moderate NaI absorption line. We derived its effective temperature and surface gravity of 2700-2800 K and 4.0-4.5, respectively, by comparing the observed spectra with synthesized spectra of low-mass objects. The location of DH Tau B on the HR diagram gives its mass of 30-50 Jupiter mass.