We present optical and near infrared observations of GRB 080325 classified as a Dark GRB. Near-infrared observations with Subaru/MOIRCS provided a clear detection of afterglow in Ks band, although no optical counterpart was reported. The flux ratio of rest-wavelength optical to X-ray bands of the afterglow indicates that the dust extinction along the line of sight to the afterglow is Av = 2.7 - 10 mag. This large extinction is probably the major reason for optical faintness of GRB 080325. The J - Ks color of the host galaxy, (J - Ks = 1.3 in AB magnitude), is significantly redder than those for typical GRB hosts previously identified. In addition to J and Ks bands, optical images in B, Rc, i, and z bands with Subaru/Suprime-Cam were obtained at about one year after the burst, and a photometric redshift of the host is estimated to be z_{photo} = 1.9. The host luminosity is comparable to L^{*} at z sim 2 in contrast to the sub-L^{*} property of typical GRB hosts at lower redshifts. The best-fit stellar population synthesis model for the host shows that a large dust extinction (Av = 0.8 mag) attributes to the red nature of the host and that the host galaxy is massive (M_{*} = 7.0 times 10^{10} Msun) which is one of the most massive GRB hosts previously identified. By assuming that the mass-metallicity relation for star-forming galaxies at z sim 2 is applicable for the GRB host, this large stellar mass suggests the high metallicity environment around GRB 080325, consistent with inferred large extinction.
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