Photometric and spectroscopic observations of the peculiar Type Ib Supernova 1991D are presented. SN 1991D was exceptionally bright for a Type Ib supernova. The He I lines were rather weak and the velocity at the photosphere as a function of time was unusually low. Comparison of the observed and synthetic spectra indicates that either hydrogen was ejected with a minimum velocity of 12,000 km/s or the spectrum contained features caused by lines of Ne I. Light curve modelling suggests that the progenitor probably had a very large radius (~10^14 cm) and that a considerable amount of 56Ni was synthesized during the explosion (~0.7 Msolar). We suggest a progenitor model of SN 1991D that involves a binary system.