The Type Ia supernova (SN Ia) rate, when compared to the cosmic star formation history (SFH), can be used to derive the delay-time distribution (DTD; the hypothetical SN Ia rate versus time following a brief burst of star formation) of SNe Ia, which can distinguish among progenitor models. We present the results of a supernova (SN) survey in the Subaru Deep Field (SDF). Over a period of 3 years, we have observed the SDF on four independent epochs with Suprime-Cam on the Subaru 8.2-m telescope, with two nights of exposure per epoch, in the R, i' and z' bands. We have discovered 150 SNe out to redshift z~=2. Using 11 photometric bands from the observer-frame far-ultraviolet to the near-infrared, we derive photometric redshifts for the SN host galaxies (for 24 we also have spectroscopic redshifts). This information is combined with the SN photometry to determine the type and redshift distribution of the SN sample. Our final sample includes 28 SNe Ia in the range 1.0<z<1.5 and 10 in the range 1.5<z<2.0.