We present a catalog of the redshifts for most long-duration gamma-ray bursts (GRBs) by Swift from 2004 December 20 to 2008 July 23 (258 bursts in total). All available information is collected, including spectroscopic redshifts, photometric redshift limits, and redshifts calculated from various luminosity relations. Error bars for the redshifts derived from the luminosity relations are asymmetric, with tails extended to the high-redshift end, and this effect is evaluated by looking at the 30% of Swift bursts with spectroscopic redshifts. A simulation is performed to eliminate this asymmetric effect, and the resultant redshift distribution is deconvolved. We test and confirm this simulation on the sample of bursts with known spectroscopic redshifts and then apply it to the 70% of Swift bursts that do not have spectroscopic measures. A final intrinsic redshift distribution is then made for almost all Swift bursts, and the efficiency of the spectroscopic detections is evaluated. The efficiency of spectroscopic redshifts varies from near unity at low redshift to 0.5 at z = 1, to near 0.3 at z = 4, and to 0.1 at z = 6. We also find that the fraction of GRBs with z>5 is ∼10%, and this fraction is compared with simulations from a cosmological model.