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 K I absorption line, and a moderate Na I absorption line. We derived its effective temperature and surface gravity of Teff = 2700 -- 2800 K and log g = 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 M_Jupiter.