The CGRO/BATSE Complete Spectral Catalog of Bright Gamma-Ray Bursts (GRBs) contains the results of a systematic spectral analysis of 350 bright GRBs observed with the Burst and Transient Source Experiment (BATSE; spectral range ~ 30 keV - 2 MeV) with high temporal and spectral resolution. The sample was selected from the complete set of 2704 BATSE GRBs based on their energy fluence or peak photon flux values in order to assure good statistics, and included 17 short GRBs. To obtain well-constrained spectral parameters, several photon models were used to fit each spectrum. Spectral parameters resulting from the fits using different models were compared, and the spectral parameters that best represent each spectrum were statistically determined, taking into account the parametrization differences among the models. A thorough analysis was performed on 350 time-integrated and 8459 time-resolved burst spectra, and the effects of integration times in determining the spectral parameters were explored. Using the results, correlations among spectral parameters and their evolution pattern within each burst were studied. The resulting spectral catalog provides reliable constraints on particle acceleration and emission mechanisms in GRBs, and is the most comprehensive study of spectral properties of GRB prompt emission to date. The files containing the details of the spectral model fits to the GRBs are also available as data products associated with this Browse table. This table was created in May 2006 based on the electronic versions of Tables 1 and 9 from the published paper which were supplied by the author. This is a service provided by NASA HEASARC .